Question

At the beginning of a basketball game, a referee tosses the ball straight up with a speed of 4.41 m/s. A player cannot touch the ball until after it reaches its maximum height and begins to fall down. What is the minimum time that a player must wait before touching the ball?

Answer 1

To develop this problem we will apply the linear motion kinematic equations. For this purpose we will define the change in speed as the product between acceleration and time.

$v_f-v_i = at$

The relation between initial velocity final velocity and time is

$v_f = v_i+at$

The acceleration is due to the acceleration due to gravity, then we have

$v_f = v_i-gt$

At the maximum height the final velocity is zero. Then we have that

$0 = v_i-gt$

$t = \frac{v_i}{g}$

The time the player must wait before touching he ball is

$t = \frac{4.41}{9.8}$

$t = 0.45s$