Question

Find the rate of change of its elevation when x= 22

Answer 1

Given:

`y=-(1)/(110)x^2+127`

The horizontal component of velocity is 5 ft/s.

`(dx)/(dt)=5`

To find the rate of change,

`\begin{gathered} (dy)/(dx)=(d)/(dx)(-(1)/(110)x^2+127) \\ (dy)/(dx)=-(1)/(110)(2x)(dx)/(dt)+0 \\ (dy)/(dx)=-(1)/(110)(2x)(5) \\ (dy)/(dx)=-(x)/(11) \\ at\text{ x=22} \\ (dy)/(dx)=-(22)/(11)=-2 \end{gathered}`

So, the rate of chnage of elevation is -2 ft/s.

That means decreasing by 2 ft/s.