A girl is whirling a ball on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit the target on the other side of the yard. When should she let go of the string?

Answer 1

It should be released when the string is at 90 degrees to the target and moving towrds the target, because at that time the ball's velocity vector points in the direction of the target. It will then keep going in that direction, and at least roll there. Whether it reaches the target or not, and at what height, will depend upon the speed of the ball, the release height and the distance to the target.