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

Answer:

h_max = 12.56 units

(the exercise does no specify the units)

Step-by-step 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:

$\frac{dh(t)}{dt}=-32t+6$

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

$-32t+6=0\\\\t=\frac{6}{32}=\frac{3}{16}$

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

$h(t)=-16(\frac{3}{16})^2+6(\frac{3}{16})+12$

$h(t)=12.56$

hence, the maximum height is 12.56 units