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 10:57 PM post.
To calculate 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 start falling down.
Let's break down the problem and see how we can find the answer:
1. The initial upward velocity of the ball (when tossed) = 4.6 m/s.
2. When the ball reaches its maximum height, its velocity becomes 0.
3. The acceleration due to gravity (in this case, acting downward) = 9.8 m/s².
We can use the kinematic equation that relates velocity, acceleration, and time:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration due to gravity
t = time
Since we know the final velocity is 0 when the ball reaches its maximum height, we can plug in the values:
0 = 4.6 m/s + (-9.8 m/s²) * t
Now, we can solve for t:
-4.6 m/s = -9.8 m/s² * t
Divide both sides of the equation by -9.8 m/s²:
t = (-4.6 m/s) / (-9.8 m/s²)
Simplifying:
t ≈ 0.47 seconds
Therefore, the minimum time a player must wait before touching the ball is approximately 0.47 seconds.