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.
To find the minimum time that a player must wait before touching the ball, we need to determine the time it takes for the ball to reach its maximum height and then begin to fall down.
We can solve this problem using the equations of motion for uniformly accelerated motion, since the only force acting on the ball is gravity.
Step-by-step solution:
1. Identify the given information:
Initial velocity (u) = 4.6 m/s
Final velocity (v) at the maximum height = 0 m/s (since the ball momentarily stops at the peak)
Acceleration (a) due to gravity = -9.8 m/s^2 (negative because it acts in the opposite direction of motion)
2. Use the equation: v = u + at to find the time it takes for the ball to reach its maximum height.
0 = 4.6 + (-9.8)t
-4.6 = -9.8t
t = -4.6 / -9.8
t ≈ 0.469 seconds (rounded to three decimal places)
3. Now, we have the time it takes for the ball to reach its maximum height. To find the minimum time a player must wait before touching the ball, we double this time.
Minimum time = 2 * t
Minimum time = 2 * 0.469 seconds
Minimum time ≈ 0.938 seconds (rounded to three decimal places)
Therefore, the minimum time that a player must wait before touching the ball is approximately 0.938 seconds.