Question

A plane flying with a constant speed of 19 km/min passes over a ground radar station at an altitude of 4 km and climbs at an angle of 25 degrees. At what rate is the distance from the plane to the radar station increasing 3 minutes later?
The distance is increasing at

Answer 1

The plane's x- and y- speed is

dx/dt = 19 cos 25°
dy/dt = 19 sin 25°

At time t, the distance z is

z^2 = x^2 + (y+4)^2
so,
2z dz/dt 2x dx/dt + 2(y+4) dy/dt.

Now just figure x,y,z at t=3, and plug in the values.