Question

PLEASE HELP!! A tennis ball machine serves a ball vertically into the air from a height of two feet, with an initial speed of 120 feet per second. After how many seconds does the ball attain its maximum height? Round to the nearest whole foot

Answer 1

After 3.73 seconds ball will achieve the maximum height.

Explanation:

Initial speed of the tennis ball is u = 120 feet per second

Since at the maximum height ball's final speed will be = 0

So we will apply the formula of motion against gravitational pull

v = u - gt

Where v = speed of the ball at maximum height

u = initial speed

g = gravitational pull = 32.17 ft/sec²

t = time to achieve maximum height

Here v = 0 so

0 = 120 - (32.17)t

t = 120/32.17 = 3.73 seconds

Answer 2

Thank you for posting your question here. I hope the answer below will help.

Vo=110 feet per second
ho=2 feet
So, h(t) = -16t^2 +110t +2
Take the derivative: h'(t) = 110 -32t
The maximum height will be at the inflection when the derivative crosses the x-axis aka when h'(t)=0.
So, set h'(t)=0 and solve for t:
0 = 110 -32t
-110 = -32t
t=3.4375
t=3.44 seconds