# Solved papers for JEE Main & Advanced Physics Two Dimensional Motion JEE PYQ - Two Dimensional Relative Motion

### done JEE PYQ - Two Dimensional Relative Motion Total Questions - 33

• question_answer1) A ball whose kinetic energy is E, is projected at an angle of ${{45}^{o}}$ to the horizontal. The kinetic energy of the ball at the highest point of its flight will be                                               [AIEEE 2002]

A)
E

B)
$E/\sqrt{2}$

C)
$E/2$

D)
zero

• question_answer2) A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an angle of ${{30}^{o}}$ with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground? $[g=10\,m/{{s}^{2}},\sin {{30}^{o}}=1/2,\cos {{30}^{o}}=\sqrt{3}/2]$ [AIEEE 2003]

A)
$5.20$ m

B)
$4.33$ m

C)
$2.60$ m

D)
$8.66$ m

• question_answer3) The coordinates of a moving particle at any time t are given by $x=\alpha {{t}^{3}}$ and $y=\beta {{t}^{3}}$. The speed of the particle at time t is given by [AIEEE 2003]

A)
$3t\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}$

B)
$3{{t}^{2}}\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}$

C)
${{t}^{2}}\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}$

D)
$\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}$

• question_answer4) A projectile can have the same range R for two angles of projection. If${{T}_{1}}$and${{T}_{2}}$are the times of flights in the two cases, then the product of the two times of flights is directly proportional to     [AIEEE 2004]

A)
$\frac{1}{{{R}^{2}}}$

B)
$\frac{1}{R}$

C)
R

D)
${{R}^{2}}$

• question_answer5) A ball is thrown from a point with a speed${{v}_{0}}$at an angle of projection$\theta$. From the same point and at the same instant, a person starts running with a constant speed $\frac{{{v}_{0}}}{2}$to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection? [AIEEE 2004]

A)
Yes, $60{}^\circ$

B)
Yes,$30{}^\circ$

C)
No

D)
Yes,$45{}^\circ$

• question_answer6) A projectile can have the same range R for two angles of projection. If${{t}_{1}}$and${{t}_{2}}$are the times of flights in the two cases, then the product of the two times of flights is proportional to [AIEEE 2005]

A)
${{R}^{2}}$

B)
$\frac{1}{{{R}^{2}}}$

C)
$\frac{1}{R}$

D)
$R$

• question_answer7) A particle is moving eastwards with a velocity of$5m{{s}^{-1}}$. In 10 s, the velocity changes to$5\text{ }m{{s}^{-1}}$northwards.  The average acceleration in this time is                                        [AIEEE 2005]

A)
$\frac{1}{\sqrt{2}}m{{s}^{-2}}$towards north-east

B)
$\frac{1}{2}m{{s}^{-2}}$towards north

C)
zero

D)
$\frac{1}{\sqrt{2}}m{{s}^{-2}}$towards north-west

• question_answer8) A particle is projected at$T=2s$to the horizontal with a kinetic energy K. The kinetic energy at the highest point is                                  [AIEEE 2007]

A)
K

B)
zero

C)
K/4

D)
K/2

• question_answer9) A particle has an initial velocity of$3\hat{i}+4\hat{j}$and an acceleration of$0.4\hat{i}+0.3\hat{j}$. It speed after 10 s is: [AIEEE 2009]

A)
10 units

B)
$7\sqrt{2}$ units

C)
7 units

D)
8.5 units.

• question_answer10) A particle is moving with velocity) $\overrightarrow{v}=K(y\hat{i}+x\hat{j})$where K is a constant. The general equation for its path is    [AIEEE 2010]

A)
(a)${{y}^{2}}={{x}^{2}}+constant$

B)
$y={{x}^{2}}+constant$

C)
${{y}^{2}}=x+constant$

D)
$xy=constant$

• question_answer11)  Two fixed frictionless inclined planes making an angle$30{}^\circ$and$60{}^\circ$with the vertical are shown in the figure. Two blocks A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B?                                                        [AIEEE 2010]

A)
(a)$4.9\text{ }m{{s}^{2}}$in vertical direction

B)
(b)$4.9\text{ }m{{s}^{2}}$ in horizontal direction

C)
(c)$9.8\text{ }m{{s}^{2}}$in vertical direction

D)
Zero

• question_answer12) A particle of mass 'm' is projected with a velocity $\upsilon$ making an angle of 30° with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height 'h' is :     [AIEEE 11-05-2011]

A)
zero

B)
(b)$\frac{m{{\upsilon }^{3}}}{\sqrt{2}g}$

C)
(c)$\frac{\sqrt{3}}{16}\frac{m{{\upsilon }^{3}}}{g}$

D)
(d)$\frac{\sqrt{3}}{2}\frac{m{{\upsilon }^{2}}}{g}$

• question_answer13) A boy can throw a stone up to a maximum height of 10m. The maximum horizontal distance that the boy can throw the same stone up to will be:                                 [AIEEE 2012]

A)
$20\sqrt{2}$ m

B)
10 m

C)
$10\sqrt{2}$ m

D)
20 m

• question_answer14) A Projectile is given an initial velocity of$(\hat{i}+2\hat{j})m/s$+ where$\hat{i}$is along the ground and $\hat{j}$is along the vertical. If$g=10\text{ }m/{{s}^{2}},$the equation of its trajectory is: [JEE MAIN 2013]

A)
$y=x-5{{x}^{2}}$

B)
$y=2x-5{{x}^{2}}$

C)
$4y=2x-5{{x}^{2}}$

D)
$4y=2x-25{{x}^{2}}$

• question_answer15) A  Ball projected from ground at an angle of ${{45}^{0}}$ just clears a wall in front. If point of projection is 4m from the foot of wall and ball strikes the ground at a distance of 6 m on the other side of the wall, the height of the wall is:                   [JEE ONLINE 22-04-2013]

A)
4.4 m

B)
2.4 m

C)
3.6 m

D)
1.6 m

• question_answer16) The maximum range of a bullet fired form a toy pistol mounted on a cart at rest is ${{\operatorname{R}}_{0}}=40$ m. What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity $\upsilon =20$ m/s, on a horizontal surface? [JEE ONLINE 25-04-2013]             (g = 10 m/$\text{m/}{{\text{s}}^{\text{2}}}$)

A)
$\text{3}{{\text{0}}^{\text{0}}}$

B)
$\text{6}{{\text{0}}^{\text{0}}}$

C)
$\text{7}{{\text{5}}^{\text{0}}}$

D)
$\text{4}{{\text{5}}^{\text{0}}}$

• question_answer17) The position of a projectile launched from the origin at t = 0is given by $\vec{r}=\left( 40\hat{i}+50\hat{j} \right)m$at $t=2s.$If the projectile was launched at an angle $\theta$ from the horizontal, then $\theta$ is (take $g=10\,m{{s}^{-2}}$) [JEE ONLINE 09-04-2014]

A)
(a)${{\tan }^{-1}}\frac{2}{3}$

B)
(b)${{\tan }^{-1}}\frac{3}{2}$

C)
(c)${{\tan }^{-1}}\frac{7}{4}$

D)
(d)${{\tan }^{-1}}\frac{4}{5}$

• question_answer18) The initial speed of a bullet fired from a rifle is 630 m/s. The rifle is fired at the centre of a target 700 m away at the same level as the target. How far above the centre of the target? [JEE ONLINE 11-04-2014]

A)
1.0m

B)
4.2 m

C)
6.1 m

D)
9.8 m

• question_answer19) A person climbs up a stalled escalator in 60 s. If standing on the same but escalator running with constant velocity he takes 40 s. How much time is taken by the person to walk up the moving escalator? [JEE ONLINE 12-04-2014]

A)
37 s

B)
27 s

C)
24 s

D)
45 s

• question_answer20) A particle is moving with a velocity $\overrightarrow{v}=K\left( y\,\,\overrightarrow{i}+x\,\,\overrightarrow{j} \right)$, where K is a constant. The general equation for its path is: [JEE Main 09-Jan-2019 Morning]

A)
$y={{x}^{2}}+constant$

B)
${{y}^{2}}=\text{ }{{x}^{2}}+constant$

C)
${{y}^{2}}=\,\,x+constant$

D)
$xy\text{ }=\text{ }constant$

• question_answer21)  The position co-ordinates of a particle moving in a 3-D coordinate system is given by $~x=a\text{ }cos\omega t$ $y=a\text{ }sin\omega t$ and $z=a\omega t$ The speed of the particle is: [JEE Main 09-Jan-2019 Evening]

A)
$a\omega$

B)
$\sqrt{3}\,a\omega$

C)
$\sqrt{2}\,a\omega$

D)
$2\,a\omega$

• question_answer22) Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is- [JEE Main 10-Jan-2019 Morning]

A)
1 : 16

B)
1 : 8

C)
1 : 2

D)
1 : 4

• question_answer23) A body is projected at t = 0 with a velocity $10\,m\,{{s}^{-1}}$ at an angle of $60{}^\circ$ with the horizontal. The radius of curvature of its trajectory at t = 1 s is R. Neglecting air resistance and taking acceleration due to gravity $g=10\,m\,{{s}^{-2}},$the value of R is- [JEE Main 11-Jan-2019 Morning]

A)
2.5 m

B)
2.8 m

C)
10.3 m

D)
5.1 m

• question_answer24) A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr, The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction, and (ii) in the opposite direction is- [JEE Main 12-Jan-2019 Morning]

A)
(a)$\frac{25}{11}$

B)
(b)$\frac{3}{2}$

C)
(c)$\frac{5}{2}$

D)
(d)$\frac{11}{5}$

• question_answer25) A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60° with ground level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is [JEE Main 12-Jan-2019 Morning]

A)
v

B)
$\frac{\sqrt{3}}{2}v$

C)
(c)$\frac{2v}{\sqrt{3}}$

D)
(d)$\frac{v}{2}$

• question_answer26)  Two particles A, B are moving on two concentric circles of radii ${{R}_{1}}$and ${{R}_{2}}$with equal angular speed$\omega$. At t = 0, their positions and direction of motion are shown in the figure. [JEE Main 12-Jan-2019 Evening] The relative velocity ${{\vec{v}}_{A}}-{{\vec{v}}_{B}}$at $t=\frac{\pi }{2\omega }$is given by

A)
(a)$-\omega ({{R}_{1}}+{{R}_{2}})\hat{i}$

B)
(b)$\omega ({{R}_{1}}-{{R}_{2}})\hat{i}$

C)
(c)$\omega ({{R}_{2}}-{{R}_{1}})\hat{i}$

D)
(d)$-\omega ({{R}_{1}}+{{R}_{2}})\hat{i}$

• question_answer27)  Four particles A, B, C and D with masses ${{m}_{A}}=m,{{m}_{B}}=2m,$${{m}_{C}}=3m$and ${{m}_{D}}=4m$are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is :    [JEE Main 8-4-2019 Morning]

A)
(a)$\frac{a}{5}\left( \hat{i}-\hat{j} \right)$

B)
(b)$\frac{a}{5}\left( \hat{i}+\hat{j} \right)$

C)
Zero

D)
(d)$a\left( \hat{i}+\hat{j} \right)$

• question_answer28) Ship A is sailing towards north-east with velocity $\text{\vec{v}=30\hat{i}+50\hat{j}}\,\text{km/hr}$ where $\text{\hat{i}}$ points east and $\hat{j},$ north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 km/hr. A will be at minimum distance from B in:      [JEE Main 8-4-2019 Morning]

A)
4.2 hrs.

B)
2.2 hrs.

C)
3.2 hrs.

D)
2.6 hrs.

• question_answer29) The stream of a river is flowing with a speed of 2km/h. A swimmer can swim at a speed of 4km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight? [JEE Main 9-4-2019 Morning]

A)
$60{}^\circ$

B)
$150{}^\circ$

C)
$90{}^\circ$

D)
$120{}^\circ$

• question_answer30)  A plane is inclined at an angle $\alpha =30{}^\circ$with a respect to the horizontal. A particle is projected with a speed $u=2m{{s}^{-1}}$from the base of the plane, making an angle $\theta ={{15}^{o}}$with respect to the plane as shown in the figure. The distance from the base, at which the particle hits the plane is close to : (Take $g=10\,m{{s}^{-2}}$) [JEE Main 10-4-2019 Afternoon]

A)
14 cm

B)
20 cm

C)
18 cm

D)
26 cm

• question_answer31) The trajectory of a projectile near the surface of the earth is given as $y=2x-9{{x}^{2}}.$. If it were launched at an angle ${{\theta }_{0}}$with speed ${{\text{v}}_{0}}$then $\left( g=10\text{ }m{{s}^{2}} \right)$: [JEE Main Held on 12-4-2019 Morning]

A)
(a)${{\theta }_{0}}={{\cos }^{-1}}\left( \frac{1}{\sqrt{5}} \right)$and${{\text{v}}_{0}}=\frac{5}{3}m{{s}^{-1}}$

B)
(b)${{\theta }_{0}}={{\sin }^{-1}}\left( \frac{1}{\sqrt{5}} \right)$and${{\text{v}}_{0}}=\frac{5}{3}m{{s}^{-1}}$

C)
(c)${{\theta }_{0}}={{\sin }^{-1}}\left( \frac{2}{\sqrt{5}} \right)$and${{\text{v}}_{0}}=\frac{3}{5}m{{s}^{-1}}$

D)
(d)${{\theta }_{0}}={{\cos }^{-1}}\left( \frac{2}{\sqrt{5}} \right)$and${{\text{v}}_{0}}=\frac{3}{5}m{{s}^{-1}}$

• question_answer32) Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights,${{h}_{1}}$and ${{h}_{2}}.$Which of the following is correct? [JEE Main 12-4-2019 Afternoon]

A)
(a)${{R}^{2}}=2\,{{h}_{1}}{{h}_{2}}$

B)
(b)${{R}^{2}}=16\,{{h}_{1}}{{h}_{2}}$

C)
(c)${{R}^{2}}=4\,{{h}_{1}}{{h}_{2}}$

D)
(d)${{R}^{2}}=\,{{h}_{1}}{{h}_{2}}$

• question_answer33) A particle is moving along the x-axis with its coordinate with time t given by $x\left( t \right)=10+8t3{{t}^{2}}.$ Another particle is moving along the y-axis with its coordinate as a function of time given by $y\left( t \right)=58{{t}^{3}}.$ $At\text{ }t=1\text{ }s,$ the speed of the second particle as measured in the frame of the first particle is given as $\sqrt{v}$ . Then v (in m/s) is ________. [JEE MAIN Held On 08-01-2020 Morning]