Question

You are jumping off the 12-foot diving board at the municipal pool. You bounce up at 6 feet per second and drop to the water. Your height (h) in feet above the water in terms of (t) seconds is given by h = -16t^2 + 6t + 12. What is the first step in determining the maximum height that you reach during your dive?

Answer 1

h_max = 12.56 units

(the exercise does no specify the units)

Explanation:

You have the following function:

`h(t)=-16t^2+6t+12` (1)

To calculate the maximum height reach by you, you first derivative the function h(t) respect to t:

`(dh(t))/(dt)=-32t+6`

Next, you equal the result of the derivative to zero and you obtain t:

`-32t+6=0\\\\t=(6)/(32)=(3)/(16)`

Then, you replace this value of t in the equation (1) and you obtain the maximum height:

`h(t)=-16((3)/(16))^2+6((3)/(16))+12`

`h(t)=12.56`

hence, the maximum height is 12.56 units