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

V = Vo + g*t = 0 at max. h.

4.6 - 9.8t = 0

To determine the minimum time a player must wait before touching the ball, we need to first find the time it takes for the ball to reach its maximum height.

We can solve this problem using the equations of motion for vertical motion. The initial vertical velocity is 4.6 m/s, and the acceleration due to gravity is -9.8 m/s² (taking positive upward). The ball will reach its maximum height when its vertical velocity becomes zero.

The equation for the final velocity in vertical motion is given by:

v = u + at

Where:
v = final velocity
u = initial velocity
a = acceleration
t = time

In this case, the final velocity is 0 m/s, the initial velocity is 4.6 m/s, and the acceleration is -9.8 m/s². Plugging these values into the equation, we can solve for time:

0 = 4.6 + (-9.8)t

Rearranging the equation:

9.8t = 4.6

Dividing both sides by 9.8:

t = 4.6 / 9.8 ≈ 0.469 seconds

Therefore, it will take approximately 0.469 seconds for the ball to reach its maximum height.

Since the player cannot touch the ball until after it reaches its maximum height and begins to fall down, the minimum time the player must wait before touching the ball is approximately 0.469 seconds.