At the beginning of a basketball game, the referee tosses the ball straight up with a speed of 4.6m/s. A player cannot touch the basketball until it has reached maximum height and begins to fall back down. What is the minimum time a player must wait before touching the ball?

t=0.47s

Explanation:

the ball has uniformly accelerated movement due to gravity

Vo=initial speed=4.6m/s

g=gravity=-9.8m/s^2

Vf=final speed=0, the player must wait for the ball to stop. so the final speed will be 0

we can use the following ecuation

T = (Vf-Vo) / g

T = (0-4.6) / -9.8m/s^2

T=0.47s