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question_answer1) A body is projected at \[t=0\] with a velocity \[10\text{ }m{{s}^{-1}}\] at an angle of \[60{}^\circ \] with the horizontal. The radius of curvature of its trajectory at \[t=1s\] is Rm. Neglecting air resistance and taking acceleration due to gravity \[g=10\text{ }m{{s}^{-2}}\], the value of R is:
question_answer2) A particle is moving along a circular path with a constant speed of\[10\text{ }m{{s}^{-1}}\]. What is the magnitude of the change in velocity (in m/s) of the particle, when it moves through an angle of \[60{}^\circ \] around the centre of the circle?
question_answer3) A particle moves from the point \[(2.0\hat{i}+4.0\hat{j})m\], at \[t=0\], with an initial velocity \[\left( 5.0\hat{i}+4.0\hat{j} \right)m{{s}^{-1}}\]. It is acted upon by a constant force which produces a constant acceleration \[\left( 4.0\hat{i}+4.0\hat{j} \right)m{{s}^{-2}}\]. What is the distance (in metre) of the particle from the origin at time 2s?
question_answer4) Ship A is sailing towards north-east with velocity \[v=30\hat{i}+50\hat{j}\,km/hr\] where \[\hat{i}\] 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 _____ hours.
question_answer5) The position vector of a particle changes with time according to the relation \[\vec{r}\left( t \right)=15{{t}^{2}}\hat{i}+\left( 4-20{{t}^{2}} \right)\hat{j}.\] What is the magnitude of the acceleration (in \[m/{{s}^{2}}\]) at t =1?
question_answer6) A plane is inclined at an angle \[\alpha =30{}^\circ \] with respect to the horizontal. A particle is projected with a speed \[u=2\text{ }m{{s}^{-1}}\] from the base of the plane, as shown in figure. The distance (in metre) from the base, at which the particle hits the plane is close to: \[\left( Take\text{ }g=10\text{ }m{{s}^{-2}} \right)\]
question_answer7) The angle between the two vectors \[\vec{A}=3\hat{i}+4\hat{j}+5\hat{k}\] and \[\vec{B}=3\hat{i}+4\hat{j}-5\hat{k}\] will be
question_answer8) A vector is represented by \[3\hat{i}+\hat{j}+2\hat{k}\]. Projection of this vector in XY plane is
question_answer9) The resultant of two vectors \[\vec{A}\] and \[\vec{B}\] is perpendicular to the vector \[\vec{A}\] and its magnitude is equal to half the magnitude of vector \[\vec{B}\]. The angle between \[\vec{A}\] and \[\vec{B}\] is
question_answer10) A person aiming to reach the exactly opposite point on the bank of a stream is swimming with a speed of 0.5 m/s at an angle of \[120{}^\circ \] with the direction of flow of water. The speed (in m/s) of water in the stream is
question_answer11) The horizontal range of a projectile is \[4\sqrt{3}\] times its maximum height. Its angle of projection will be
question_answer12) 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 \[\theta \] should be:
question_answer13) A body is thrown horizontally from the top of a tower of height 5 m. It touches the ground at a distance of 10 m from the foot of the tower. The initial velocity (in m/s) of the body is \[\left( g=10m{{s}^{-2}} \right)\]
question_answer14) At the height 80 m, an aeroplane is moving with a speed of 150 m/s. A bomb is dropped from it so as to hit a target. At what distance (in metre) from the target should the bomb be dropped \[\left( given\text{ }g=10\text{ }m/{{s}^{2}} \right)\]
question_answer15) Two bodies are thrown up at angles of \[45{}^\circ \] and \[60{}^\circ \] respectively, with the horizontal. If both bodies attain same vertical height, then the ratio of velocities with which these are thrown is \[\sqrt{\frac{x}{2}}\] . Find the value of x.
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