Standing on a long railroad car, a boy throws a ball straight upwards. The car travels on a horizontal road with an acceleration of 1 m/s ^2 , and the projection velocity in the vertical direction is 9.8 m/s . Find how far behind the boy the ball will fall on the car, in m.

Step-by-step solution

The time of flight of the ball is given by T = 2u_y g . Substituting u_y = 9.8 m/s and g = 9.8 m/s ^2 , we get T = 2 9.8 9.8 = 2 s . In the horizontal direction, the ball moves with a constant velocity equal to the velocity of the car at the instant of projection. The car accelerates horizontally with a = 1 m/s ^2 . The relative horizontal acceleration of the ball with respect to the car is a_ rel = -1 m/s ^2 . The initial relative horizontal velocity is u_ rel = 0 . The horizontal displacement of the ball relative