A plane flying horizontally at an altitude of 2 mi and a spe

A plane flying horizontally at an altitude of 2 mi and a speed of 510 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.)
mi/h

Solution

Let r is the shortest distance between plane and station and x is horizontal distance.

then by pythagoras : r^2 = 2^2 + x^2 ==> r = (2^2 + 5^2) = (29)

differentiate with respect to t:
2r dr/dt = 2x dx/dt

(dr/dt)= (x/r)* dx/dt = (5/(29))* 510 = 473.52 mi/h