A plane, flying horizontally at an altitude of 1 km and a speed of 500 km/hr, passes directly over a radar station. find the rate in km/hr at which the distance from the plane to the station is changing when it is 2 km away from the radar station. Hint: this is not a max/min problem. into what category of problems does this problem belong?

Question

Steve · Answer

this is a related rates problem.

When the plane is x km (horizontally) away from the station, the distance y from the plane to the station is

y^2 = 1^2 + x^2
When x=2, y^2 = 5

So, we now know what we need.

2y dy/dt = 2x dx/dt
2√5 dy/dt = 2*2*500
dy/dt = 200√5 km/hr