A plane flying with a constant speed of 4 km/min passes over a ground radar station at an altitude of 5 km and climbs at an angle of 45 degrees. At what rate, in km/min is the distance from the plane to the radar station increasing 4 minutes later?

Question

A plane flying with a constant speed of  4 km/min passes over a ground radar station at an altitude of 5 km and climbs at an angle of 45 degrees. At what rate, in km/min is the distance from the plane to the radar station increasing 4  minutes later?

drwls · Answer

I know of no plane that can climb at a 45 degree angle for 4 minutes at 4 km/minute. It would be at altitude 21 km at that time.

Planes that slow (159 mph) do not fly that high.

X = 2.828 t
Y = 5 + 2.828 t

Distance to radar station = D
= sqrt(X^2 + Y^2)
= sqrt(8t^2 + 25 + 28.28t + 8 t^2)
- sqrt(16t^2 + 28.28t + 25)

Solve for dD/dt at plug in t = 4

Solve for