Question

SCALCET8 3.9.013. A plane flying horizontally at an altitude of 2 mi and a speed of 570 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 5 mi away from the station. (Round your answer to the nearest whole number.)

Answer 1

DL/dt = 529 miles/h

Explanation:

The radio station (point A) the point just up the radio station ( point B), and the variable position of the plane ( at specif t point C) shape a right triangle wich hypothenuse L is:

L² = d² + x²

d is the constant distance between the plane and the ground

Then differentiation with respect to time on both sides of the equation

2*L*dL/dt = 2*d* Dd/dt + 2*x*dx/dt

But Dd/dt = 0

L*dL/dt = x*dx/dt

x = 5 miles dx/dt = 570 m/h L = √ d² + x² L √ (5)² + (2)²

L = √29 L = 5.39 m

5.39 *DL/dt = 5*570 m/h

DL/dt = 5*570/5.39 miles/h

DL/dt = 528.76 miles/h

DL/dt = 529 miles/h