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

h = 110.24 m

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
`(dh)/(dt)=0`

So,

`(d( -16t^2 + 84t))/(dt)=0\\\\-32t+84=0\\\\t=(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.