Problem 47.

A tennis ball is thrown vertically upward with an initial velocity of +8.0 m/s.

(a) what will the ball\'s speed be when it returns to its starting point?

(b) how long will the ball take to reach its starting point?

Solution:

This is the free fall motion with constant acceleration. The equations which describe this motion are the following:

where we introduced an axis y with upward direction. The origin of axis y is the initial position of the ball. The initial velocity of the ball is 8 m/s.

(a) The final point is the starting point. It means that the coordinate of the final point is 0. We substitute this coordinate in the third equation and obtain:

It means that the magnitude of the final velocity is 8 m/s. The direction of the final velocity is downward. So we should write

Minus sign means that the direction is downward.

(b) To find the traveled time we substitute the final position (0 m) in the first equation of the system and obtain:

Then