Question

A plane flying with a constant speed of 180 km/h passes over a ground radar station at an altitude of 2 km and climbs at an angle of 30°. At what rate is the distance from the plane to the radar station increasing a minute later? (Round your answer to the nearest whole number.)

Answer 1

Here is an outline on how to do this, using calculus

all units in km. d is how far the plane moved in 1 minute (180 km/hour * 1/60 hour)
r is the distance between the plane and the station

using the law of cosines:
\[ r^2= d^2 + 2^2 - 2dcos(120º) \]
solve for r when d= 3 km (one min of flying)

take the derivative wrt time:
\[2 r \frac{dr}{dt}= 2 d \frac{dd}{dt} + \frac{dd}{dt}\]

the plane is moving at dd/dt (sorry about choosing d!) = 3 km/min
plug r, dd/dt, d into the equation and solve for dr/dt