Question

I hit a baseball while it is 2.5 feet above the ground. If at the time the ball was hit, it was moving upwards at a speed of 85 ft/s. How high up will the ball go?

Answer 1

The ball will reach a maximum height of approximately 112.79 ft.

Step-by-step explanation:

To determine how high the ball will go, we need to calculate the maximum height it will reach. We can start by finding the time it takes for the ball to reach its peak height. Using the equation v = u + at, where v is the final velocity (0 ft/s at the peak height), u is the initial velocity (85 ft/s), a is the acceleration due to gravity (-32.2 ft/s^2), and t is the time, we can solve for t.

0 = 85 - 32.2t

t = 85/32.2 ≈ 2.6438 s

Next, we can find the maximum height using the equation h = ut + 0.5at^2, where h is the height, u is the initial velocity, a is the acceleration due to gravity, and t is the time.

h = 85(2.6438) + 0.5(-32.2)(2.6438)^2

h ≈ 112.79 ft