Question

Find the rate of change of its elevation when x=32

Answer 1

From the question

We are given the equation

`y=-(1)/(80)x^2+90`

The horizontal component of the velocity is a constant of 5ft/s

We are to find the rate of change of its elevation at x = 32

First, we will differentiate the equation with respect to t

This gives

`(dy)/(dt)=-(2)/(80)x\text{.}(dx)/(dt)`

Since the horizontal component of the velocity is a constant of 5ft/s

Then

`(dx)/(dt)=5ft\/s`

Since x = 32

Hence we have

`(dy)/(dt)=-(2)/(80)(32)(5)`

Simplifying this we get

`(dy)/(dt)=4`

Therefore, the rate of change of its elevation is 4ft/s