Question

Ronin kicks a ball over the gate of the first floor balcony. The function h(t)=-36t^2+288t+9 can be used to model the height of the ball where t is the time in seconds after the ball kicked and h(t) is the height in feet 1. Find the time in Devon which the ball reaches it maximum height

Answer 1

Answer: 4 seconds

Step-by-step explanation:

Given: The function $h(t)=-36t^2+288t+9$ can be used to model the height of the ball where t is the time in seconds after the ball kicked and h(t) is the height in feet.

Differentiate the given function with respect to t , we get

$h'(t)=-36(2)t+288=-72t+288$

Put h'(t)=0

$\Rightarrow\ -72t+288=0\Rightarrow\ t=\dfrac{288}{72}\\\\\Rightarrow\ t=4$

Also, $h''(t)=-72<0$

By second derivative test, h(t) is maximum at t=4.

Hence, the time in Devon which the ball reaches it maximum height = 4 seconds