Question

You are trying to dunk a basketball. You need to jump 2.5ft in the air to dunk the ball. The height that your feet are above the ground is given by the function h(t) = -16t^2 +12t. What is the maximum height your feet will be above the ground? Will you be able to dunk the basketball ?

Answer 1

Step-by-step explanation:

The height that your feet are above the ground is given by the function :

$h(t) = -16t^2 +12t$ ...(1)

We need to find the maximum height your feet will be above the ground.

For maximum height, put dh(t)/dt = 0

$\dfrac{dh}{dt}=0\\\\\dfrac{d( -16t^2 +12t)}{dt}=0\\\\-32t+12=0\\\\t=0.375\ s$

Now put t = 0.375 s in equation (1) as follows :

$h(t)=-16\left(0.375\right)^{2}+12\left(0.375\right)\\\\=2.25\ ft$

So, the feet will be 2.25 feet above the ground. Yes, you will be able to dunk the basketball.