Question

A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.

Answer 1

`250\sqrt 3mi/h`

Step-by-step explanation:

Altitude,h=1 mi

Speed,v=
`(dx)/(dt)=`500mi/h

We have to find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.

`y^2=x^2+h^2=x^2+1`

y=2 mi

`2^2=x^2+1`

`4-1=x^2`

`3=x^2`

`x=\sqrt 3`mi

Differentiate w.r. t

`2y(dy)/(dt)=2x(dx)/(dt)+0`

`y(dy)/(dt)=x(dx)/(dt)`

`(dy)/(dt)=(x)/(y)(dx)/(dt)`

`(dy)/(dt)=(\sqrt 3)/(2)* 500=250\sqrt 3mi/h`