JEE Main & Advanced Physics Two Dimensional Motion Question Bank

Self Evaluation Test - Motion in a Plane Total Questions - 100

1)

If a unit vector is represented by \[0.5\widehat{i}+0.8\widehat{j}+c\widehat{k}\,,\] then the value of c is

A)
1

B)
                   \[\sqrt{0.8}\]

C)
\[\sqrt{0.11}\]

D)
       \[\sqrt{0.01}\]
View Solution
2)

If the magnitudes of vectors A, B and C are 12, 5 and 13 units respectively and A + B = C, the angle between vectors A and B is:

A)
0

B)
       \[\pi \]

C)
\[\frac{\pi }{2}\]

D)
       \[\frac{\pi }{4}\]
View Solution
3)

The velocity of a projectile at the initial point A is \[\left( 2\widehat{i}\text{ }+\text{ }3\widehat{j} \right)\]m/s its velocity (in m/s) at point B is

A)
\[-2\widehat{i}\text{ }+\text{ }3\widehat{j}\]

B)
       \[2\widehat{i}-3\widehat{j}\]

C)
\[2\widehat{i}+3\widehat{j}\]

D)
\[-2\widehat{i}-3\widehat{j}\]
View Solution
4)

A body is projected from the ground with a velocity at an angle of \[30{}^\circ \]. It crosses a wall after 3 sec. How far beyond the wall the stone will strike the ground? [Take \[\text{g =10 m/}{{\text{s}}^{\text{2}}}\]]

A)
50\[\sqrt{2}\]

B)
       70\[\sqrt{2}\]

C)
15\[\sqrt{3}\]

D)
       16\[\sqrt{2}\]
View Solution
5)

A stone is projected horizontally with a \[\text{5 m/s}\] from the top of a plane inclined at an angle \[45{}^\circ \] with the horizontal. How far from the point of projection will the particle strike the plane?

A)
5\[\sqrt{2}\]m

B)
       11\[\sqrt{2}\]m

C)
12\[\sqrt{2}\]m

D)
       15\[\sqrt{2}\]m
View Solution
6)

Two balls are projected at an angle \[\theta \] and \[(90{}^\circ -\theta )\] to the horizontal with the same speed. The ratio of their maximum vertical heights is B Tricky

A)
1:1

B)
       \[\text{tan}\theta :1\]

C)
\[1:\text{tan}\theta \]

D)
       \[\text{ta}{{\text{n}}^{2}}\theta :1\]
View Solution
7)

A body is thrown with a velocity of \[9.8\text{ }m{{s}^{-1}}\] making an angle of \[30{}^\circ \] with the horizontal. It will hit the ground after a time

A)
3.0 s

B)
       2.0 s

C)
1.5 s

D)
                   1 s
View Solution
8)

The velocity of projection of a body is increased by 2%. Other factors remaining unchanged, what will be the percentage change in the maximum height attained?

A)
1%

B)
       2%

C)
4%

D)
       8%
View Solution
9)

A cricket ball is hit with a velocity \[25\text{ }m{{s}^{-1}}\], \[60{}^\circ \] above the horizontal. How far above the ground, ball passes over a fielder 50 m from the bat (consider the ball is struck very close to the ground)?

Take \[\sqrt{3}=\text{1}\text{.7 }\]and \[\text{g = 10 m}{{\text{s}}^{-2}}\]

A)
6.8 m

B)
       7 m

C)
5 m

D)
       10 m
View Solution
10)

A stone is thrown from a point with a speed 5 m/s at an elevation angle of \[\theta \]. From the same point and at the same instant, a person starts running with a constant speed 2.5 m/s to catch the stone. If the person will be able to catch the ball then, what should be the angle of projection \[\theta \]?

A)
\[75{}^\circ ~~\]

B)
       \[30{}^\circ \]

C)
\[60{}^\circ \]

D)
       \[45{}^\circ \]
View Solution
11)

If the resultant of the vectors \[3\widehat{i}+4\widehat{j}+5\widehat{k}\] and \[5\widehat{i}\text{ }+\text{ }3\widehat{j}\text{ }+\text{ }4\widehat{k}\] makes an angle \[\theta \] with x-axis, then \[cos\text{ }90{}^\circ \] is

A)
0.07

B)
       0.574

C)
0.111

D)
       0.123
View Solution
12)

Let \[\overrightarrow{C}=\overrightarrow{A}+\overrightarrow{B}\] then

A)
\[|\overrightarrow{C}|\] is always greater than \[|\overrightarrow{A}|\]

B)
it is possible to have \[|\overrightarrow{C}|\,<\,|\overrightarrow{A}|\] and \[|\overrightarrow{C}|\,\,<\,\,|\overrightarrow{B}|\]

C)
\[\overrightarrow{C}\] is always equal to \[\overrightarrow{A}+\overrightarrow{B}\]

D)
\[\overrightarrow{C}\] is never equal to \[\overrightarrow{A}+\overrightarrow{B}\]
View Solution
13)

Vector \[\overrightarrow{A}\] makes equal angle with x, y and z-axis. Value of its components in terms of magnitude of \[\overrightarrow{A}\] will be

A)
\[\frac{\overrightarrow{A}}{\sqrt{3}}\]

B)
       \[\frac{\overrightarrow{A}}{\sqrt{2}}\]

C)
\[\sqrt{3}\,\overrightarrow{A}\]

D)
       \[\frac{\sqrt{3}}{\overrightarrow{A}}\]
View Solution
14)

The vector that must be added to the vector \[\widehat{i}-3\widehat{j}+2\widehat{k}\] and \[3\widehat{i}-6\widehat{j}+7\widehat{k}\] so that the resultant vector is a unit vector along the y-axis, is

A)
\[4\widehat{i}-2\widehat{j}+5\widehat{k~}~~\]

B)
\[-\,4\widehat{i}-2\widehat{j}+5\widehat{k~}~~\]

C)
\[3\widehat{i}-4\widehat{j}+5\widehat{k~}~~\]

D)
Null vector
View Solution
15)

It is found that \[|A+B|\,=\,|A|\]. This necessarily implies,

A)
\[B=0\]

B)
A, B are antiparallel

C)
A, B are perpendicular

D)
\[A,\text{ }B\le 0\]
View Solution
16)

The resultant of two vectors \[\overrightarrow{A}\] and \[\overrightarrow{B}\] is perpendicular to the vector \[\overrightarrow{A}\] and its magnitude is equal to half the magnitude of vector \[\overrightarrow{B}\]. The angle between \[\overrightarrow{A}\] and \[\overrightarrow{B}\] is

A)
\[120{}^\circ \]

B)
\[150{}^\circ \]

C)
\[135{}^\circ \]

D)
\[180{}^\circ \]
View Solution
17)

If \[\overrightarrow{A}=\overrightarrow{B}-\overrightarrow{C}\], then, the angle between \[\overrightarrow{A}\] and \[\overrightarrow{B}\] is

A)
\[\text{ta}{{\text{n}}^{-1}}\frac{{{B}^{2}}+{{A}^{2}}-{{C}^{2}}}{2AB}\]

B)
\[{{\sin }^{-1}}\frac{{{B}^{2}}+{{A}^{2}}-{{C}^{2}}}{2AB}\]

C)
\[{{\cos }^{-1}}\frac{{{A}^{2}}+{{B}^{2}}-{{C}^{2}}}{2AB}\]

D)
\[{{\sec }^{-1}}\frac{{{A}^{2}}+{{B}^{2}}-{{C}^{2}}}{2AB}\]
View Solution
18)

The resultant of vectors \[\overrightarrow{\text{P}}\text{ }\]and \[\overrightarrow{\text{Q}}\] is \[\overrightarrow{\text{R}}\]. On reversing the direction of \[\overrightarrow{\text{Q}}\], the resultant vector becomes \[\overrightarrow{S}\]. Then, correct relation is

A)
\[~{{R}^{2}}+{{S}^{2}}=({{P}^{2}}+{{Q}^{2}})\]

B)
\[{{R}^{2}}+{{S}^{2}}={{P}^{2}}+{{Q}^{2}}\,\]

C)
\[{{R}^{2}}+{{P}^{2}}={{S}^{2}}+{{Q}^{2}}\]

D)
\[{{P}^{2}}+{{S}^{2}}=2\,({{Q}^{2}}+{{R}^{2}})\]
View Solution
19)

The x and y components of \[\overrightarrow{\text{A}}\] are 4 m and 6 m, respectively. The x and y components of \[(\overrightarrow{A}+\overrightarrow{B}\,)\]are 10 m and 9 m respectively. The magnitude of vector B is:

A)
19 m

B)
       \[\sqrt{27}\]

C)
\[\sqrt{45}\]

D)
       \[\sqrt{50}\]
View Solution
20)

If the sum of two unit vectors is a unit vector, then the magnitude of their difference is

A)
1

B)
       \[\sqrt{2}\]

C)
\[\sqrt{3}\]

D)
       2
View Solution
21)

If \[A=5\widehat{i}+7\widehat{j}-3\widehat{k}\] and \[B=2\widehat{i}+2\widehat{j}-a\widehat{k}\] are perpendicular vectors, the value of a is:

A)
\[-\,2\]

B)
       8

C)
\[-\,7\]

D)
       \[-\,8\]
View Solution
22)

The condition for \[\overrightarrow{A}+\overrightarrow{B}\] to be perpendicular to \[\overrightarrow{A}-\overrightarrow{B}\] is that

A)
\[|\overrightarrow{A}|\,\,=\,\,|\overrightarrow{B}|\]

B)
       \[\overrightarrow{\text{A}}\,\,\text{=}\,\,\overrightarrow{\text{B}}\]

C)
\[\overrightarrow{\text{B}}\text{ =}\,\,\text{0 }\!\!~\!\!\text{ }\]

D)
       \[\text{ }\!\!|\!\!\text{ }\,\overrightarrow{\text{A}}\,\text{+}\,\overrightarrow{\text{B}}\,\text{ }\!\!|\!\!\text{ }\,\,\text{= }\!\!|\!\!\text{ }\,\overrightarrow{\text{A}}-\overrightarrow{\text{B}}\,\,\text{ }\!\!|\!\!\text{ }\]
View Solution
23)

Let \[\vec{a}\] and \[\vec{b}\] be two unit vectors. If the vectors \[\vec{c}=\hat{a}+2\hat{b}\] and \[\vec{d}=\,\,5\hat{a}-2\hat{b}\] are perpendicular to each other, then the angle between \[\hat{a}\] and \[\hat{b}\] is:

A)
\[\frac{\pi }{6}\]

B)
       \[\frac{\pi }{2}\]

C)
\[\frac{\pi }{3}\]

D)
       \[\frac{\pi }{4}\]
View Solution
24)

A particle crossing the origin of co-ordinates at time t = 0, moves in the xy-plane with a constant acceleration a in the y-direction. If its equation of motion is \[\text{y = b}{{\text{x}}^{\text{2}}}\] (b is a constant), its velocity component in the x-direction is

A)
\[\sqrt{\frac{2\text{b}}{\text{a}}}\]

B)
       \[\sqrt{\frac{\text{a}}{2\text{b}}}\]

C)
\[\sqrt{\frac{\text{a}}{\text{b}}}\]

D)
       \[\sqrt{\frac{\text{b}}{\text{a}}}\]
View Solution
25)

The position of particle is given by \[\vec{r}=2\,{{t}^{2}}\widehat{i}+3\,t\widehat{j}+4\widehat{k},\] where \[t\] is in second and the coefficients have proper units for \[\vec{r}\] to be in meter. The \[\vec{a}\,(t)\] of the particle at \[t=1s\,\] is

A)
\[\text{4}\,\text{m }{{\text{s}}^{-2}}\] along y-direction

B)
\[\text{3}\,\text{m }{{\text{s}}^{-2}}\] along x-direction

C)
\[\text{4 m }{{\text{s}}^{-2}}\] along x-direction

D)
\[\text{2 m }{{\text{s}}^{-2}}\] along z-direction
View Solution
26)

A particle has an initial velocity \[3\hat{i}+\text{ }4\hat{j}\] and an acceleration of \[0.4\,\hat{i}+0.3\hat{j}\]. Its speed after 10 sec is

A)
7\[\sqrt{2}\]units

B)
7 units

C)
8.5 units

D)
       10 units
View Solution
27)

A particle moves in the X-Y plane with a constant acceleration \[1.5\text{ }m/{{s}^{2}}\] in the direction making an angle of \[37{}^\circ \] with the X-axis. At \[t=0\] the particle is at the origin and its velocity is 8.0 m/s along the X-axis. Find the position of the particle at \[t=4.0\text{ }s\].

A)
(41.6 m, 7.2 m)

B)
     (50.3 m, 8.2 m)

C)
(60.2 m, 8.2 m)

D)
       (11.2 m, 8 m)
View Solution
28)

The coordinates of a particle moving in x-y plane at any instant of time t are \[\text{x = 4}{{\text{t}}^{\text{2}}}\text{; y = 3}{{\text{t}}^{\text{2}}}\]. The speed of the particle at that instant is

A)
10 t

B)
       5 t

C)
3 t

D)
       2 t
View Solution
29)

A bullet is dropped from the same height when another bullet is fired horizontally They will hit the ground

A)
one after the other

B)
simultaneously

C)
depends on the observer

D)
None of these
View Solution
30)

If \[{{V}_{1}}\] is velocity of a body projected from the point A and \[{{V}_{2}}\] is the velocity of a body projected from point B which is vertically below the highest point C. if both the bodies collide, then

A)
\[{{\text{V}}_{\text{1}}}\text{=}\frac{\text{1}}{\text{2}}{{\text{V}}_{\text{2}}}\]

B)
\[{{\text{V}}_{2}}\text{=}\frac{\text{1}}{\text{2}}{{\text{V}}_{1}}\]

C)
\[\,{{\text{V}}_{\text{1}}}\text{=}{{\text{V}}_{\text{2}}}\]

D)
Two bodies can't collide.
View Solution
31)

Which of the following is correct?

A)
\[\vec{A}\,.\,\vec{B}\ne \vec{B}\,.\,\vec{A}\]

B)
\[\vec{A}\,.(\vec{B}+\vec{C})=\vec{A}\,.\,\vec{B}+\vec{C}\]

C)
\[\vec{A}\times \vec{B}\ne \vec{B}\times \vec{A}\]

D)
\[\vec{A}\,.(\vec{B}+\vec{C})\ne \vec{A}\,.\,\vec{B}+\vec{A}\,.\,\vec{C}\]
View Solution
32)

If none of the vectors \[\vec{A},\,\,\vec{B}\] and \[\vec{C}\] are zero and if \[\vec{A}\times \vec{B}=0\],\[\vec{B}\times \vec{C}=0\] the value of \[\vec{A}\times \vec{C}\] is:

A)
unity

B)
       zero

C)
\[{{B}^{2}}\]

D)
       \[AC\text{ }cos\theta \]
View Solution
33)

If \[|\vec{A}\times \vec{B}|\,=\sqrt{3}\,\vec{A}\,.\,\vec{B}\,,\] then the value of \[|\vec{A}+\vec{B}|\] is:

A)
\[{{\left( {{\text{A}}^{\text{2}}}\text{+}{{\text{B}}^{\text{2}}}\text{+}\frac{\text{AB}}{\sqrt{\text{3}}} \right)}^{1/2}}\]

B)
\[\text{A+B}\]

C)
\[{{\left( {{\text{A}}^{\text{2}}}\text{+}{{\text{B}}^{\text{2}}}\text{+}\sqrt{\text{3}}\text{AB} \right)}^{1/2}}\]

D)
\[{{\left( {{\text{A}}^{\text{2}}}\text{+}{{\text{B}}^{\text{2}}}\text{+AB} \right)}^{1/2}}\]
View Solution
34)

\[\overrightarrow{a}=3\,\hat{i}-5\hat{j}\] and \[\overrightarrow{b}=6\,\hat{i}+3\,\hat{j}\] are two vectors and \[\overrightarrow{c}\] is a vector such that \[\overrightarrow{c}=\overrightarrow{a}\times \overrightarrow{b}\] then \[|\overrightarrow{a}|:|\overrightarrow{b}|:|\overrightarrow{c}|\]

A)
\[\sqrt{34}:\sqrt{45}:\sqrt{39}\]

B)
\[\sqrt{34}:\sqrt{45}:39\]

C)
\[34\text{ }:\text{ }39\text{ }:\text{ }45\]

D)
\[39\text{ }:\text{ }35\text{ }:\text{ }34\]
View Solution
35)

If \[|\vec{a}|\,=4,\,\,|\vec{b}|\,=2\] and the angle between \[\vec{a}\] and \[\vec{b}\] is \[\pi /6\] then \[{{(\overrightarrow{a}\times \overrightarrow{b})}^{2}}\] is equal to

A)
48

B)
       16

C)
4

D)
       2
View Solution
36)

If the vectors \[(\hat{i}+\hat{j}+\hat{k})\] and \[3\hat{i}\] form two sides of a triangle, the area of the triangle is:

A)
\[\sqrt{3}\]

B)
       \[2\sqrt{3}\]

C)
\[\frac{3}{\sqrt{2}}\]

D)
       \[3\sqrt{2}\]
View Solution
37)

The vector having magnitude equal to 3 and perpendicular to the two vectors \[\vec{A}=2\hat{i}+2\hat{j}+\hat{k}\] and \[\vec{B}=2\hat{i}-2\hat{j}+3\hat{k}\] is:

A)
\[\pm \,(2\hat{i}-\hat{j}-2\hat{k})~~~\]

B)
\[\pm \,(3\hat{i}+\hat{j}-2\hat{k})\]

C)
\[-\,(3\hat{i}+\hat{j}-3\hat{k})~\]

D)
\[(3\hat{i}-\hat{j}-3\hat{k})\]
View Solution
38)

Let two vectors \[\vec{A}=3\hat{i}+\hat{j}+2\hat{k}\] and\[\vec{B}=2\hat{i}-2\hat{j}+4\hat{k}\]. Consider the unit vector perpendicular to both A and B is

A)
\[\frac{\hat{i}-\hat{j}-\hat{k}}{\sqrt{3}}\]

B)
       \[\frac{\hat{i}-\hat{j}-\hat{k}}{2\sqrt{3}}\]

C)
\[\frac{-\hat{i}-\hat{j}-\hat{k}}{\sqrt{3}}\]

D)
       \[\frac{\hat{i}-\hat{j}-\hat{k}}{2\sqrt{3}}\]
View Solution
39)

A projectile can have the same range R for two angles of projection. If \[{{t}_{1}}\] and \[{{t}_{2}}\] be the times of flight in two cases, then what is the product of two times of flight?

A)
\[{{\text{t}}_{\text{1}}}{{\text{t}}_{\text{2}}}\propto \text{R}\]

B)
       \[{{\text{t}}_{\text{1}}}{{\text{t}}_{\text{2}}}\propto {{\text{R}}^{2}}\]

C)
\[{{\text{t}}_{\text{1}}}{{\text{t}}_{\text{2}}}\propto 1/\text{R}\]

D)
       \[{{\text{t}}_{\text{1}}}{{\text{t}}_{\text{2}}}\propto 1/{{\text{R}}^{2}}\]
View Solution
40)

A particle of mass m is projected with a velocity u making an angle of \[30{}^\circ \] with the horizontal. The magnitude of\[({{V}_{h}}\times h)\] of the projectile when the particle is at its maximum height h

A)
\[\frac{\sqrt{3}}{2}\frac{{{\text{v}}^{\text{2}}}}{\text{g}}\]

B)
       zero

C)
\[\frac{{{\text{v}}^{\text{2}}}}{\sqrt{2}\text{g}}\]

D)
       \[\frac{\sqrt{3}}{16}\frac{{{\text{v}}^{\text{2}}}}{\text{g}}\]
View Solution
41)

The range of a projectile is R when the angle of projection is \[40{}^\circ \]. For the same velocity of projection and range, the other possible angle of projection is

A)
\[45{}^\circ \]

B)
       \[50{}^\circ \]

C)
\[60{}^\circ \]

D)
       \[40{}^\circ \]
View Solution
42)

If the angles of projection of a projectile with same initial velocity exceed or fall short of \[45{}^\circ \] by equal amounts , then the ratio of horizontal ranges is

A)
\[1\text{ }:\text{ }2\]

B)
       \[1\text{ }:\text{ }3~\]

C)
\[1\text{ }:\text{ }4\]

D)
       \[1\text{ }:\text{ }1\]
View Solution
43)

The equation of a projectile is \[y=\sqrt{3}x-\frac{\text{g}{{\text{x}}^{2}}}{20}\] The angle of projection is given by

A)
\[\text{tan}\theta \,\text{=}\frac{1}{\sqrt{3}}\]

B)
       \[\text{tan}\theta \,\text{=}\,\sqrt{3}\]

C)
\[\frac{\pi }{2}\]

D)
zero.
View Solution
44)

A plane flying horizontally at a height of 1500 m with a velocity of \[200\text{ m}{{\text{s}}^{-1}}\] passes directly overhead on antiaircraft gun. Then the angle with the horizontal at which the gun should be fired from the shell with a muzzle velocity of 400 \[\text{m}{{\text{s}}^{-1}}\]to hit the plane, is

A)
\[90{}^\circ \,\]

B)
                   \[60{}^\circ \]

C)
\[30{}^\circ \]

D)
       \[45{}^\circ \]
View Solution
45)

The equation of trajectory of projectile is given by\[y=\frac{x}{\sqrt{3}}-\frac{\text{g}{{\text{x}}^{2}}}{20}\], where x and y are in meter. The maximum range of the projectile is

A)
\[\frac{8}{3}\text{ m}\]

B)
\[\frac{4}{3}\text{ m}\]

C)
\[\frac{3}{4}\text{ m}\]

D)
\[\frac{3}{8}\text{ m}\]
View Solution
46)

A bullet is fired with a speed of \[1500\text{ }m\text{/}s\] in order to hit a target 100 m away. If \[g=10\text{ }m\text{/}{{s}^{2}}.\]The gun should be aimed

A)
15 cm above the target

B)
10 cm above the target

C)
2.2 cm above the target

D)
directly towards the target
View Solution
47)

A projectile is thrown in the upward direction making an angle of \[\,60{}^\circ \] with the horizontal direction with a velocity of \[147\text{ }m{{s}^{-1}}\]. Then the time after which its inclination with the horizontal is \[45{}^\circ \], is

A)
15 s

B)
       10.98 s

C)
5.49 s

D)
       2.74 s
View Solution
48)

Two pegs A and B thrown with speeds in the ratio 1:3 acquired the same heights. If A is thrown at an angle of \[30{}^\circ \] with the horizontal, the angle of projection of B will be

A)
\[0{}^\circ \]

B)
       \[si{{n}^{-1}}\left( \frac{1}{8} \right)\]

C)
\[si{{n}^{-1}}\left( \frac{1}{6} \right)\]

D)
       \[si{{n}^{-1}}\left( \frac{1}{2} \right)\]
View Solution
49)

A body projected at an angle with the horizontal has a range 300 m. If the time of flight is 6 s, then the horizontal component of velocity is

A)
\[30\text{ m}\,\,{{\text{s}}^{-1}}\]

B)
       \[50\text{ m}\,\,{{\text{s}}^{-1}}\]

C)
\[40\text{ m}\,\,{{\text{s}}^{-1}}\]

D)
       \[45\text{ m}\,\,{{\text{s}}^{-1}}\]
View Solution
50)

A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be

A)
20\[\sqrt{2}\] m

B)
       10 m

C)
10\[\sqrt{2}\]m

D)
20 m
View Solution
51)

A projectile is given an initial velocity of \[\left( \hat{i}\text{ }+\text{ }2\text{ }\hat{j} \right)\text{ }m/s\], where; is along the ground and j is along the vertical. If \[g=10\text{ }m/{{s}^{2}}\], the equation of its trajectory is :

A)
\[y=x-5{{x}^{2}}\]

B)
       \[y=2x-5{{x}^{2}}\]

C)
\[4y=2x-5{{x}^{2~}}~\]

D)
       \[4y=2x-25{{x}^{2}}\]
View Solution
52)

A body is projected vertically upwards with a velocity u, after time t another body is projected vertically upwards from the same point with a velocity v, where v < u. If they meet as soon as possible, then choose the correct option

A)
\[t=\frac{u-v+\sqrt{{{u}^{2}}+{{v}^{2}}}}{g}\]

B)
\[t=\frac{u-v+\sqrt{{{u}^{2}}-{{v}^{2}}}}{g}\]

C)
\[t=\frac{u+v+\sqrt{{{u}^{2}}-{{v}^{2}}}}{g}\]

D)
\[t=\frac{u-v+\sqrt{{{u}^{2}}-{{v}^{2}}}}{2g}\]
View Solution
53)

A particle is projected with a velocity v such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where g is acceleration due to gravity)

A)
\[\frac{4{{v}^{2}}}{5g}\]

B)
       \[\frac{4g}{5{{v}^{2}}}\]

C)
\[\frac{{{v}^{2}}}{g}\]

D)
       \[\frac{4{{v}^{2}}}{\sqrt{5}g}\]
View Solution
54)

A projectile is fired from the surface of the earth with a velocity of 5 \[m{{s}^{-1}}\,\] and angle \[\theta \] with the horizontal. Another projectile fired from another planet with a velocity of 3 \[m{{s}^{-1}}\,\]at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in \[\text{m}{{\text{s}}^{-2}}\]) given \[\text{g = 9}\text{.8 m/}{{\text{s}}^{\text{2}}}\]

A)
3.5

B)
       5.9

C)
163

D)
       110.8
View Solution
55)

A projectile is thrown at an angle of \[40{}^\circ \] with the horizontal and its range is \[{{R}_{1}}\]. Another projectile is thrown at an angle \[40{}^\circ \] with the vertical and its range is \[{{R}_{2}}\]. What is the relation between \[{{R}_{1}}\] and \[{{R}_{2}}\]?

A)
\[{{R}_{1}}={{R}_{2}}\]

B)
       \[{{R}_{1}}=2{{R}_{2}}\]

C)
\[2{{R}_{1}}={{R}_{2}}\]

D)
       \[{{R}_{1}}=4{{R}_{2}}/5\]
View Solution
56)

A particle is projected at an angle of elevation \[\alpha \] and after t seconds it appears to have an angle of elevation \[\beta \] as seen from point of projection. The initial velocity will be

A)
\[\frac{gt}{2\sin \left( \alpha -\beta \right)}\]

B)
       \[\frac{gt\,\cos \beta }{2\sin \left( \alpha -\beta \right)}\]

C)
\[\frac{\sin \left( \alpha -\beta \right)}{2gt}\]

D)
       \[\frac{2\sin \left( \alpha -\beta \right)}{gt\,\cos \beta }\]
View Solution
57)

A projectile is thrown in the upward direction making an angle of \[60{}^\circ \] with the horizontal direction with a velocity of 147\[m{{s}^{-1}}\]. Then the time after which its inclination with the horizontal is \[45{}^\circ \], is

A)
\[15\left( \sqrt{3}-1 \right)\text{s}\]

B)
       \[15\left( \sqrt{3}+1 \right)\text{s}\]

C)
\[7.5\left( \sqrt{3}-1 \right)\text{s}\]

D)
       \[7.5\left( \sqrt{3}+1 \right)\text{s}\]
View Solution
58)

If a particle is projected with speed u from ground at an angle with horizontal, then radius of curvature of a point where velocity vector is perpendicular to initial velocity vector is given by

A)
\[\frac{{{u}^{2}}{{\cos }^{2}}\theta }{g}\]

B)
       \[\frac{{{u}^{2}}{{\cot }^{2}}\theta }{g\sin \theta }\]

C)
\[\frac{{{u}^{2}}}{g}\]

D)
       \[\frac{{{u}^{2}}{{\tan }^{2}}\theta }{g\cos \theta }\]
View Solution
59)

A ball rolls off to the top of a staircase with a horizontal velocity u m/s. If the steps are h meter high and b meter wide, the ball will hit the edge of the nth step, if

A)
\[n=\frac{2hu}{g{{b}^{2}}}\]

B)
       \[n=\frac{2h{{u}^{2}}}{gb}\]

C)
\[n=\frac{2h{{u}^{2}}}{g{{b}^{2}}}\]

D)
       \[n=\frac{h{{u}^{2}}}{g{{b}^{2}}}\]
View Solution
60)

A body of mass m is projected horizontally with a velocity v from the top of a tower of height h and it reaches the ground at a distance x from the foot of the tower. If a second body of mass 2m is projected horizontally from the top of a tower of height 2h, it reaches the ground at a distance 2x from the foot of the tower. The horizontal velocity of the second body is

A)
\[~v\]

B)
       \[2v\]

C)
\[\sqrt{2v}\]

D)
       \[v/2\]
View Solution
61)

A bomb is dropped on an enemy post by an aero plane flying horizontally with a velocity of \[60\text{ }km\text{ }{{h}^{-1}}\] and at a height of 490 m. At the time of dropping the bomb, how far the aero plane should be from the enemy post so that the bomb may directly hit the target?

A)
\[\frac{400}{3}\text{m}\]

B)
       \[\frac{500}{3}\text{m}\]

C)
\[\frac{1700}{3}\text{m}\]

D)
       \[\text{498}\,\text{m}\]
View Solution
62)

A projectile of mass m is thrown with a velocity v making an angle \[60{}^\circ \] with the horizontal. Neglecting air resistance, the change in velocity from the departure A to its arrival at B, along the vertical direction is

A)
2v

B)
       \[\sqrt{3}\text{v}\]

C)
v

D)
       \[\frac{\text{v}}{\sqrt{3}}\]
View Solution
63)

A particle is projected at angle \[37{}^\circ \] with the incline plane in upward direction with speed 10 m/s. The angle of incline plane is given \[53{}^\circ \]. Then the maximum height attained by the particle from the incline plane will be

A)
3 m

B)
       4 m

C)
5 m

D)
       zero
View Solution
64)

An aircraft moving with a speed of 250 m/s is at a height of 6000 m, just overhead of an anti. Aircraft gun. If the muzzle velocity is 500 m/s, the firing angle q should be:

A)
\[30{}^\circ \]

B)
       \[45{}^\circ \]

C)
\[60{}^\circ \]

D)
       \[75{}^\circ \]
View Solution
65)

A particle is projected with a certain velocity at an angle \[\alpha \] above the horizontal from the foot of an inclined plane of inclination \[30{}^\circ \]. If the particle strikes the plane normally then a is

A)
\[30{}^\circ +\text{ta}{{\text{n}}^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]

B)
       \[30{}^\circ +\text{ta}{{\text{n}}^{-1}}\left( \frac{1}{2} \right)\]

C)
\[30{}^\circ +\text{ta}{{\text{n}}^{-1}}1\]

D)
       \[60{}^\circ \]
View Solution
66)

A cricket ball thrown across a field is at heights \[{{h}_{1}},\] and \[{{h}_{2}}\] from point of projection at times \[{{t}_{1}}\] and \[{{t}_{2}}\] respectively after the throw. The ball is caught by a fielder at the same height as that of projection. The time of flight of the ball in this journey is

A)
\[\frac{{{h}_{1}}t_{2}^{2}-{{h}_{2}}t_{1}^{2}}{{{h}_{1}}{{t}_{2}}-{{h}_{2}}{{t}_{1}}}\]

B)
       \[\frac{{{h}_{1}}t_{2}^{2}+{{h}_{2}}t_{1}^{2}}{{{h}_{1}}{{t}_{2}}+{{h}_{2}}{{t}_{1}}}\]

C)
\[\frac{{{h}_{1}}{{t}_{2}}}{{{h}_{1}}{{t}_{2}}-{{h}_{2}}{{t}_{1}}}\]

D)
None
View Solution
67)

You throw a ball with a \[\text{\vec{v}}=\left( 3\hat{i}+4\hat{j} \right)\,\,\text{m/s}\] towards a wall, where it hits at height \[{{h}_{1}}\]. Suppose that the launch velocity were, instead, \[\text{\vec{v}}=\left( 5\hat{i}+4\hat{j} \right)\text{m/s}\] and \[{{h}_{2}}\] is height, then

A)
\[{{\text{h}}_{\text{1}}}\text{=}{{\text{h}}_{\text{2}}}\]

B)
\[{{\text{h}}_{\text{2}}}\text{}{{\text{h}}_{\text{1}}}\]

C)
\[{{\text{h}}_{\text{2}}}\text{}{{\text{h}}_{1}}\]

D)
       \[{{\text{h}}_{\text{2}}}\ge {{\text{h}}_{\text{1}}}\]
View Solution
68)

If retardation produced by air resistance of projectile is one-tenth of acceleration due to gravity, the time to reach maximum height

A)
decreases by 11 percent

B)
increases by 11 percent

C)
decreases by 9 percent

D)
increases by 9 percent
View Solution
69)

For a stone thrown from a lower of unknown height, the maximum range for a projection speed of 10 m/s is obtained for a projection angle of \[30{}^\circ .\] The corresponding distance between the foot of the lower and the point of landing of the stone is

A)
\[10\text{ }m\]

B)
\[~20\text{ }m\]

C)
\[\left( \text{20/}\sqrt{3} \right)\text{ m }\!\!~\!\!\text{ }\]

D)
\[\left( 10/\sqrt{3} \right)\text{ m}\]
View Solution
70)

A jet plane flying at a constant velocity v at a height \[h=8\text{ }km\], is being tracked by a radar R located at O directly below the line of flight. If the angle \[\theta \] is decreasing at the rate of \[0.025\text{ }rad/s\], the velocity of the plane when \[\theta =\text{ }60{}^\circ \]is:

A)
1440 km/h

B)
       960 km/h

C)
1920 km/h

D)
       480 km/h
View Solution
71)

An object is projected with a velocity of \[20\text{ }m/s\] making an angle of \[45{}^\circ \] with horizontal. The equation for the trajectory is \[h=Ax-B{{x}^{2}}\] where h is height, x is horizontal distance, A and B are constants. The ratio A: B is \[\left( \text{g = 10 m}{{\text{s}}^{-2}} \right)\]

A)
\[1\text{ }:\text{ }5\]

B)
       \[5\text{ }:\text{ }1~~\]

C)
\[1\text{ }:\text{ }40\]

D)
       \[40\text{ }:\text{ }1\]
View Solution
72)

The position of a projectile launched from the origin at \[t=0\]is given by \[\vec{r}=(40\hat{i}+50\hat{j})m\] at 2s. If the projectile was launched at an angle \[\theta \] from the horizontal, then \[\theta \] is (take \[\text{g = 10 m}{{\text{s}}^{-2}}\])

A)
\[{{\tan }^{-1}}\frac{2}{3}\]

B)
       \[{{\tan }^{-1}}\frac{3}{2}\]

C)
\[{{\tan }^{-1}}\frac{7}{4}\]

D)
       \[{{\tan }^{-1}}\frac{4}{5}\]
View Solution
73)

A particle is projected from a tower as shown in figure, then the distance from the foot of the tower where it will strike the ground will be

A)
4000/3 m

B)
       2000/m

C)
1000/3 m

D)
       2500/3 m
View Solution
74)

For an observer on trolley direction of projection of particle is shown in the figure, while for observer on ground ball rise vertically. The maximum height reached by ball from trolley is

A)
10 m

B)
       15 m

C)
20 m

D)
       5 m
View Solution
75)

A particle P is projected from a point on the surface of smooth inclined plane (see figure). Simultaneously another particle Q is released on the smooth inclined plane from the same position. P and Q collide on the inclined plane after \[t=4\] second. The speed of projection of P is

A)
5 m/s

B)
       10 m/s

C)
15 m/s

D)
       20 m/s
View Solution
76)

A large number of bullets are fired in all directions with the same speed v. What is the maximum area on the ground on which these bullets will spread?

A)
\[\frac{\pi {{\text{v}}^{2}}}{\text{g}}\]

B)
       \[\frac{\pi {{\text{v}}^{4}}}{{{\text{g}}^{2}}}\]

C)
\[{{\pi }^{2}}\frac{{{\text{v}}^{2}}}{{{\text{g}}^{2}}}\]

D)
       \[\frac{{{\pi }^{2}}{{\text{v}}^{4}}}{{{\text{g}}^{2}}}\]
View Solution
77)

Two particles are projected simultaneously from the level ground as shown in figure. They may collide after a time:

A)
\[\frac{x\sin {{\theta }_{2}}_{\,}}{{{u}_{1}}}\]

B)
\[\frac{x\text{ cos}{{\theta }_{2}}_{\,}}{{{u}_{2}}}\]

C)
\[\frac{x\sin {{\theta }_{2}}_{\,}}{{{u}_{1}}\sin \left( {{\theta }_{2}}-{{\theta }_{1}} \right)}\]

D)
\[\frac{x\sin {{\theta }_{1}}_{\,}}{{{u}_{2}}\sin \left( {{\theta }_{2}}-{{\theta }_{1}} \right)}\]
View Solution
78)

A body is thrown horizontally with a velocity \[\sqrt{2gh}\] from the top of a tower of height h. It strikes the level ground through the foot of the tower at a distance x from the tower. The value of x is

A)
\[h\]

B)
       \[h/2\]

C)
\[~2h~\]

D)
       \[2h/3\]
View Solution
79)

Three particles A, B and C are thrown from the top of a tower with the same speed. A is thrown up, B is thrown down and C is horizontally. They hit the ground with speeds \[{{\text{v}}_{\text{A}}}\], \[{{\text{v}}_{\text{B}}}\] and \[{{\text{v}}_{\text{C}}}\] respectively then,

A)
\[{{\text{v}}_{\text{A}}}\text{=}{{\text{v}}_{\text{B}}}\text{=}{{\text{v}}_{\text{C}}}\]

B)
       \[{{\text{v}}_{\text{A}}}\text{=}{{\text{v}}_{\text{B}}}\text{}{{\text{v}}_{\text{C}}}\]

C)
\[{{\text{v}}_{\text{A}}}\text{}{{\text{v}}_{\text{C}}}\text{}{{\text{v}}_{\text{B}}}\]

D)
       \[{{\text{v}}_{\text{A}}}\text{}{{\text{v}}_{\text{B}}}\text{=}{{\text{v}}_{\text{C}}}\]
View Solution
80)

It was calculated that a shell when fired from a gun with a certain velocity and at an angle of elevation \[5\pi /36\] rad should strike a given target. In actual practice, it was found that a hill just prevented the trajectory. At what angle (rad) of elevation should the gun be fired to hit the target

A)
\[\frac{5\pi }{36}\]

B)
       \[\frac{11\pi }{36}\]

C)
\[\frac{7\pi }{36}\]

D)
       \[\frac{13\pi }{36}\]
View Solution
81)

A boy is standing on a cart moving along x-axis with the speed of 10 m/s. When the cart reaches the origin he throws a stone in the horizontal x-y plane with the speed of 5 m/s with respect to himself at an angle \[\theta \] with the x-axis. It is found that the stone hits a ball lying at rest at a point whose co-ordinates are\[\left( \sqrt{3}\,m,\text{ }1\,m \right)\]. The value of \[\theta \] is (gravitational effect is to be ignored)

A)
\[30{}^\circ \]

B)
       \[60{}^\circ \]

C)
\[90{}^\circ \]

D)
       \[120{}^\circ \]
View Solution
82)

A projectile is fired with a velocity v at right angle to the slope which is inclined at an angle \[\theta \] with the horizontal. The range of the projectile along the inclined plane is:

A)
\[\frac{2{{\text{v}}^{\text{2}}}\tan \theta }{\text{g}}\]

B)
       \[\frac{{{\text{v}}^{\text{2}}}\sec \theta }{\text{g}}\]

C)
\[\frac{2{{\text{v}}^{\text{2}}}\tan \theta \sec \theta }{\text{g}}\]

D)
       \[\frac{{{\text{v}}^{\text{2}}}sin\theta }{\text{g}}\]
View Solution
83)

A boat is moving with a velocity \[3\text{ }\hat{i}+4\text{ \hat{j}}\] with respect to ground. The water in the river is moving with a velocity \[-3\text{ }\hat{i}-4\text{ \hat{j}}\] with respect to ground. The relative velocity of the boat with respect to water is

A)
\[8\hat{j}\]

B)
                   \[-6\hat{i}-8\hat{j}\]

C)
\[6\hat{i}+8\hat{j}\]

D)
       \[5\sqrt{2}\]
View Solution
84)

A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in \[km/hr\,\]is

A)
3

B)
       4

C)
\[\sqrt{21}\]

D)
       1
View Solution
85)

A swimmer wants to cross a river straight. He swim at \[5\text{ }km/hr\] in still water. A river 1 km wide flows at the rate of 3 km/hr. Which of the following figure shows the correct direction for the swimmer along which he should strike? (\[{{V}_{s}}\to \] velocity of swimmer, \[{{V}_{r}}\to \] velocity of river, \[V\to \] resultant velocity)

A)

B)

C)

D)

View Solution
86)

If \[{{\text{V}}_{\text{r}}}\] is the velocity of rain falling vertically and \[{{\text{V}}_{\text{m}}}\] is the velocity of a man walking on a level road, and \[\theta \] is the angle with vertical at which he should hold the umbrella to protect himself than the relative velocity of rain w.r.t. the man is given by:

A)
\[{{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}+{{\text{V}}_{\text{m}}}^{2}+2{{\text{V}}_{r}}{{\text{V}}_{\text{m}}}\cos \theta }\]

B)
\[{{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}+{{\text{V}}_{\text{m}}}^{2}-2{{\text{V}}_{r}}{{\text{V}}_{\text{m}}}\cos \theta }\]

C)
\[{{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}+{{\text{V}}_{\text{m}}}^{2}}\]

D)
\[{{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}-{{\text{V}}_{\text{m}}}^{2}}\]
View Solution
87)

An aircraft executes a horizontal loop of radius km with a steady speed of \[900\text{ }km/h\]. The ratio of centripetal acceleration to acceleration due to gravity is \[\left[ \text{g = 9}\text{.8 m/}{{\text{s}}^{\text{2}}} \right]\]

A)
6.38

B)
       9.98

C)
11.33

D)
       12.13
View Solution
88)

A boat B is moving upstream with velocity 3 m/s with respect to ground. An observer standing on boat observes that a swimmer S is crossing the river perpendicular to the direction of motion of boat. If river flow velocity is 4 m/s and swimmer crosses the river of width 100 m in 50 sec, then

A)
velocity of swimmer w.r.t ground is \[\surd 13\,\,m\text{/}s\]

B)
drift of swimmer along river is zero

C)
drift of swimmer along river will be 50 m

D)
velocity of swimmer w.r.t ground is 2 m/s
View Solution
89)

Two particles A and B separated by a distance 2R are moving counter clockwise along the same circular path of radius R each with uniform speed v. At time \[t=0\], A is given a tangential acceleration of magnitude \[\alpha =\frac{\text{77}{{\text{v}}^{2}}}{25\pi \text{R}}\] then

A)
the time lapse for the two bodies to collide is \[\frac{6\pi \text{R}}{5\text{v}}\]

B)
the angle covered by A is 11\[\pi \]/6

C)
angular velocity of A is \[\frac{11\text{v}}{5\text{R}}\]

D)
radial acceleration of A is \[\text{289 }{{\text{v}}^{\text{2}}}\text{/5R}\]
View Solution
90)

The length of second's hand in a watch is 1 cm. The change in velocity of its tip in 15 seconds is:

A)
zero

B)
\[\frac{\pi }{30\sqrt{2}}\text{ cm/s}\]

C)
\[\frac{\pi }{30}\text{ cm/s}\]

D)
       \[\frac{\pi \sqrt{2}}{30}\text{ cm/s}\]
View Solution
91)

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolution in 44 seconds, what is the magnitude and direction of acceleration of the stone?

A)
\[{{\pi }^{2}}\text{m}{{\text{s}}^{-2}}\] and direction along the radius towards the center.

B)
\[{{\pi }^{2}}\text{m}{{\text{s}}^{-2}}\] and direction along the radius away from the center.

C)
\[{{\pi }^{2}}\text{m}{{\text{s}}^{-2}}\] and direction along the tangent to the circle.

D)
\[{{\pi }^{2}}\text{/4m}{{\text{s}}^{-2}}\] and direction along the radius towards the center.
View Solution
92)

A particle moves in a circle of radius 30 cm. Its linear speed is given by: \[V=2t\], where t in second and v in m/s. Find out its radial and tangential acceleration at t = 3 sec respectively.

A)
\[\text{220 m/se}{{\text{c}}^{\text{2}}}\text{, 50 m/se}{{\text{c}}^{\text{2}}}\]

B)
\[\text{110 m/se}{{\text{c}}^{\text{2}}}\text{, 5 m/se}{{\text{c}}^{\text{2}}}\]

C)
\[\text{120 m/se}{{\text{c}}^{\text{2}}}\text{, 2 m/se}{{\text{c}}^{\text{2}}}\]

D)
\[\text{110 m/se}{{\text{c}}^{\text{2}}}\text{, 10 m/se}{{\text{c}}^{\text{2}}}\]
View Solution
93)

Three points are located at the vertices of an equilateral triangle whose side equal to a. They all start moving simultaneously with velocity v constant in modulus, with first point heading continually for the second, the second for the third, and the third for the first. How soon will the points converge?

A)
\[3v/2a\]

B)
       \[2a/5v\]

C)
\[5v/3a\]

D)
       \[~2a/3v\]
View Solution
94)

A man in a row boat must get from point A to point B on the opposite bank of the river (see figure). The distance\[BC=\text{ }a\]. The width of the river\[AC=b\]. At what minimum speed u relative to the still water should the boat travel to reach the point B? The velocity of flow of the river is \[{{v}_{0}}\].

A)
\[\sqrt{{{\text{a}}^{2}}\text{+}{{\text{b}}^{2}}}/{{\text{v}}_{0}}\]

B)
\[\frac{{{\text{v}}_{0}}\text{b}}{\sqrt{{{\text{a}}^{2}}\text{+}{{\text{b}}^{2}}}}\]

C)
\[{{\text{v}}_{0}}\,\text{a/b}\]

D)
\[{{\text{v}}_{0}}\,\text{b/a}\]
View Solution
95)

Rain, pouring down at an angle\[\alpha \]with the vertical has a speed of \[10\text{ m}{{\text{s}}^{-1}}.\] A girl runs against the rain with a speed of \[\text{8 m}{{\text{s}}^{-1}}\] and sees that the rain makes an angle \[\beta \] with the vertical, then relation between \[\alpha \] and \[\beta \] is

A)
\[\tan \alpha =\frac{8+10\sin \beta }{10\cos \beta }\]

B)
\[\tan \beta =\frac{8+10\sin \alpha }{10\cos \alpha }\]

C)
\[\tan \alpha =\tan \beta \]

D)
\[\tan \alpha =\cot \beta \]
View Solution
96)

A 2 m wide truck is moving with a uniform speed \[{{\text{v}}_{\text{0}}}\text{= 8 m/s}\] along a straight horizontal road. A pedestrain starts to cross the road with a uniform speed v when the truck is 4 m away from him. The minimum value of v so that he can cross the road safely is

A)
2.62 m/s

B)
       4.6 m/s

C)
3.57 m/s

D)
       1.414 m/s
View Solution
97)

Two boats A and B, move away from a buoy anchored at the middle of a river along the mutually perpendicular straight lines: the boat A along the river and the boat B across the river. Having moved off an equal distance from the buoy the boat returned. What is the ratio of times of motion of boats \[\frac{{{\tau }_{A}}}{{{\tau }_{B}}},\] if the velocity of each boat with respect to water is 1.2 times greater than the stream velocity?

A)
2.3

B)
       1.8

C)
0.5

D)
0.2
View Solution
98)

A balloon starts rising from the surface of the earth. The ascension rate is constant and equal to\[{{\text{v}}_{\text{0}}}\]. Due to the wind the balloon gathered the horizontal velocity component\[{{\text{v}}_{\text{x}}}\text{= ay}\], where a is a constant and y is the height of ascent. The tangential, acceleration of the balloon is trough but

A)
\[{{\text{a}}^{2}}y/{{\text{v}}_{0}}\]

B)
\[{{\text{a}}^{2}}y/\sqrt{1+{{\left( \text{ay+}{{\text{v}}_{0}} \right)}^{2}}}\]

C)
\[{{\text{a}}^{2}}y/\sqrt{1+{{\text{v}}_{0}}^{2}}\]

D)
\[{{\text{a}}^{2}}{{v}_{0}}/\sqrt{1+{{\left( \text{2y+a} \right)}^{2}}}\]
View Solution
99)

The angle which the velocity vector of a projectile thrown with a velocity v at an angle \[\theta \] to the horizontal will make with the horizontal after time t of its being thrown up is:

A)
\[\theta \]

B)
\[{{\tan }^{-1}}\left( \theta /\text{t} \right)\]

C)
\[{{\tan }^{-1}}\left( \frac{\text{v cos}\theta }{\text{v sin}\theta -\text{gt}} \right)\]

D)
\[{{\tan }^{-1}}\left( \frac{\text{v sin}\theta -\text{gt}}{\text{v cos}\theta } \right)\]
View Solution
100)

Two identical particles are projected horizontally in opposite directions with a speed of \[5\text{ m}{{\text{s}}^{-1}}\] each from the top of a tall tower as shown. Assuming \[\text{g = 10 m}{{\text{s}}^{-2}}\], the distance between them at the moment when their velocity vectors become mutually perpendicular is

A)
2.5 m

B)
5 m

C)
10 m

D)
20 m
View Solution

Study Package

Self Evaluation Test - Motion in a Plane

Buy Now

JEE Main & Advanced Physics Two Dimensional Motion Question Bank

done Self Evaluation Test - Motion in a Plane Total Questions - 100

Study Package

Self Evaluation Test - Motion in a Plane

Self Evaluation Test - Motion in a Plane Total Questions - 100