Question

The height of a soccer ball can be modeled by the function h(t) = - 8t^2 + 32t. Where h(t) is the height in feet and t is the in seconds. Find the time when the soccer ball reaches its maximum height

Answer 1

You can find the maximum using a graphing calculator. When you plug in the equation (replacing t with x), -8x²+32x. When that is plugged in to a calculator, the maximum is at 32 feet after 2 seconds.

Answer 2

At t = 2 maximum height achieved by the ball is 32 feet.

Explanation:

The height of a soccer ball can be modeled by the function h(t) = -8t² + 32t

where h(t) is the height and t is the time.

For maximum height we will find the derivative of h(t) and equate the derivative to zero.

`(d(h))/(dt)=(d(-8t^(2)+32t))/(dt)`

`(d(h))/(dt)` = -16t + 32

Now we will equate derivative
`(d(h))/(dt) = 0`

So -16t + 32 = 0

16t = 32

t = 2 seconds

At t = 2 seconds height achieved by the ball will be maximum.

Now we can calculate height h at t = 2 seconds

h(2) = -8×(2)² + 32×(2)

h(2) = -32 + 64

h(2) = 32 feet

Therefore, at t = 2 seconds soccer ball achieves the maximum height of 32 feet.