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?
See your 11:57 PM post.
Correction: See your 10:57 PM post.
4.5s
To find the minimum time that a player must wait before touching the ball, we need to calculate how long it takes for the ball to reach its maximum height.
We can use the following equation to find the time it takes for the ball to reach its maximum height:
v_f = v_i + a*t
Where:
v_f is the final velocity at maximum height (which is 0 m/s because the ball momentarily stops at its peak)
v_i is the initial velocity (4.6 m/s)
a is the acceleration due to gravity (-9.8 m/s^2)
t is the time it takes to reach maximum height (which is what we need to find)
Rearranging the equation, we have:
0 = 4.6 - 9.8*t
Simplifying further:
9.8*t = 4.6
t = 4.6 / 9.8
Using a calculator, we can calculate:
t ≈ 0.469 seconds
Therefore, the minimum time that a player must wait before touching the ball is approximately 0.469 seconds.