Question

Becky found a tennis ball outside a tennis court. She picked up the ball and threw it over the fence into

the court. The path of the tennis ball can be represented by h = -16t2 + 80t, where h represents the
height of the tennis ball in feet and t represents the time in seconds.
31. Find the maximum height of the tennis ball.
32. How long will it take for the tennis ball to hit the ground?

Answer 1

31). Maximum height = 100 feet

32). Time to hit the ground = 5 seconds

Explanation:

31). Equation modeling the height 'h' of the ball is,

h = -16t² + 80t

For the maximum height of the ball,

Find the derivative of 'h' with respect to time 't' and equate it to zero.

`(dh)/(dt)=(d)/(dt)(-16t^2+80t)`

`=-32t+80`

`(dh)/(dt)=0`

`-32t+80=0`

`t=(80)/(32)`

`t=2.5` seconds

That means after 2.5 seconds ball will reach the maximum height.

By substituting
`t=2.5` in the equation,

`h=-16(2.5)^2+80(2.5)`

`h=100` feet

Therefore, maximum height achieved by the ball is 100 feet.

32). If the ball follows the parabolic path,

Time taken by the ball to reach the maximum height = Time taken by the ball to come back to the ground from the maximum height.

Time taken by the ball to hit the ground = 2(2.5) = 5 seconds