Kinematics-07-PROBLEMS

LEVEL - IV 1. On a frictionless horizontal surface, assumed to be the x-y plane, a small y trolley A is moving along a straight line parallel to the y-axis (see figure) with A a constant velocity of  3  1 m/s. At a particular instant, when the line OA makes an angle of 45º with the x-axis, a ball is thrown along the surface from the origin O. Its velocity makes an angle  with the x-axis and it hits the trolley. O 45º x (a) The motion of the ball is observed from the frame of the trolley. Calculate the angle  made by the velocity vector of the ball with the x-axis in this frame. (b) Find the speed of the ball with respect to the surface, if   4 / 3 . 2. A large heavy box is sliding without friction down a smooth plane of inclination  . From a point P on the bottom of the box, a particle is projected inside the box. The initial speed of the particle with respect to the box is u and the direc- tion of projection makes an angle  with the bottom as shown in the figure: (a) Find the distance along the bottom of the box between the point of P and the point Q where the particle lands (Assume that the particle does not hit any other surface of the box. Neglect air resistance.] (b) If the horizontal displacement of the particle as seen by an observer on the ground is zero, find the speed of the box with respect to the ground at the instant when the particle was projected. 3. Two guns situated on the tope of a hill of height 10m fire one shot each with the same speed 5 3m / s m/s at some interval of time. One gun fires horizontally and other fires upwards at an angle of 60º with the horizontal. The shots collide in air at point P. Find : (a) The time interval between the firings and (b) The coordinates of the point P. Take origin of the coordinate system at the foot of the hill right below the muzzle and trajectories in x-y plane. 4. Two towers AB and CD are situated at a distance d apart as shown in C figure. AB is 20 m high and CD is 30 m high from the ground. An object of mass m is thrown from the top of AB horizontally with a velocity of 10 m/s towards CD. Simultaneously, another object of mass 2 m is thrown from the top of CD at an angle of 60º to the horizontal towards AB with the same A magnitude of initial velocity as that of the first object. The two objects move in the same vertical plane collide is mid-air. Calculate the distance ‘d’ be- tween the towers. B D 5. A particle is moving along the x-axis under the accelerationa(x)   m and its velocity is v = 0; (a) Find its velocity when it reaches x = 0.5 . (b) Find the time at which it reaches x = 0.5 m. 1 2x 2 . At time t =0. it is at x = 1.0