Question

A rock is thrown up from the ground at a velocity of 84 feet per second. The formula h = -16t2 + 84t gives the rock's height in feet after t second. What is the maximum height of the rock?

Answer 1

Answer:

h = 110.24 m

Step-by-step explanation:

It is given that,

A rock is thrown up from the ground at a velocity of 84 feet per second. The formula $h = -16t^2 + 84t$ gives the rock's height in feet after t second.

We need to find the maximum height of the rock. For maximum height put $\dfrac{dh}{dt}=0$

So,

$\dfrac{d( -16t^2 + 84t)}{dt}=0\\\\-32t+84=0\\\\t=\dfrac{84}{32}\\\\t=2.62\ s$

Put t = 2.62 s in the equation of height. So,

$h = -16(2.62)^2 + 84(2.62)\\\\h=110.24\ m$

So, the maximum height of the rock is 110.24 m.