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kondor19780726 [428]
2 years ago
11

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
Mathematics
1 answer:
ale4655 [162]2 years ago
3 0

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

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

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