Question #9a735

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Answer 1 · 2018-01-15T13:07:04

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

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]