Irodov Problem 1.189

The ball falls a height h freely under the influence of gravity and so looses a potential energy mgh. This will be entirely converted into its kinetic energy and hence at the time of its impact it will be traveling downwards at a speed of downwards.

Suppose that the time taken by the ball to fall this distance is t, then by this time the observer O has moved a distance Vt to the right. The time t can be calculated by using the formula for distance traveled under uniform acceleration as,



Now from the point of view of the moving observer O, at the time of impact the ball is not only falling down but also moving to the left with a velocity V. Also, from the point of view of the moving observer O the ball is located not only h units down but also Vt units to the left. In other words the location vector r and the velocity vector v of the ball as seen by the moving observer O at the time of impact are,




The angular momentum of the ball as seen from the moving observer O will be,