Question

A plane flying horizontally at an altitude of 3 mi and a speed of 460 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 4 mi away from the station (Round your answer to the nearest whole number.) 368 X mi/h Enhanced Feedback Please try again. Keep in mind that distance - (altitude)2 + (horizontal distance)? (or y = x + n ). Differentiate with respect to con both sides of the equation, using the Chain Rule, to solve for the given speed of the plane is x.

Answer 1

`(dy)/(dt)=304mi/h`

Explanation:

From the question we are told that:

Height of Plane
`h=3mi`

Speed
`(dx)/(dt)=460mi/h`

Distance from station
`d=4mi`

Generally the equation for The Pythagoras Theorem is is mathematically given by

`x^2+3^2=y^2`

For y=d

`x^2+3^2=d^2`

`x^2+3^2=4^2`

`x=√(7)`

Therefore

`x^2+3^2=y^2`

Differentiating with respect to time t we have

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

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

`(dy)/(dt)=(√(7))/(4) *460`

`(dy)/(dt)=304.2614008mi/h`

`(dy)/(dt)=304mi/h`