Question

Maria's height while jumping on a a trampoline can be modeled by the equation h=-16t^2+18t+5. Where t=time in seconds and h=height in feet. What is the maximum height that Maria will reach

Answer 1

10.06 ft

Explanation:

Maria's maximum height will occur when her velocity reaches zero (0). This means that she has stopped ascending and is about to begin descent.

The equation for the height reached by Maria on the trampoline is given as:

`h=-16t^2+18t+5`

To find her maximum height, we first have to find the time it will take her to get to that height and corresponding velocity (zero).

Her velocity can be found by differentiating her height i.e. dh/dt:

`v = (dh)/(dt) = -32t + 18`

Therefore, when v = 0:

`0 = -32t+ 18\\\\=> 32t= 18\\\\t = 18 / 32 = 0.5625 secs`

It takes her 0.5625 seconds to get to her maximum height.

Therefore, her height at that time (0.5625 seconds) is:

`h=-16(0.5625)^2+18(0.5625)+5\\\\h = -16 * (0.3164) + 10.125+5\\\\h = -5.0624 + 15.125\\\\h = 10.06 ft`

Therefore, her maximum height is 10.06 ft.