I got 356.84 km/hr for the question below, do you think this is correct?
A plane flying with a constant speed of 360 km/h passes over a ground radar station at an altitude of 3 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?
Here is my work:
2y dy/dt= 2x dx/dt + dx/dt
dy/dt= (2x+1)/2y dx/dt
dy/dt= (13/2y) *360
x= 360/60= 6 km
dy/dt= 2(6)+ 3/2 sqrt 43 *360
= (13/2sqrt 43) *360= 356.84 km/hr