Question

Question #9a735

Answer 1

The plane's distance is increasing at `330.72` miles/hour
when the plane is at `4` miles from me.

Explanation:

Let `y=3` mile altitude at which plane is flying and `y` is

constant. `z=4` mile distance from me. Let `x` be the horizontal

distance covered from iniitial position at my overhead.

`x^2+y^2= z^2 or x^2+3^2 = 4^2 :. x^2= 16-9` or

`x=sqrt7` mile `dx/dt=x'=500` mph.

`x^2+y^2= z^2` . Differentiating both sides w.r.t time `t`

we get `2x *x' +2y*y' =2z*z' or x *x' +y*y' =z*z'`

`y'=0` since `y=`constant `:. x *x' +y*0 =z*z'` or

`:. x *x' =z*z' or sqrt7 *500 = 4*z'` or

`z'= (sqrt7 *500)/4 ~~ 330.72` miles/hour

The plane's distance is increasing at `330.72` miles/hour

when the plane is at `4` miles from me. [Ans]