# Calculus

A plane flying with a constant speed of 24 km/min passes over a ground radar station at an altitude of 8 km and climbs at an angle of 20 degrees. At what rate, in km/min, is the distance from the plane to the radar station increasing 2 minutes later?

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1. I draw the figure, labeling the distance the plane flies on its path as Flightdistance(FD), d is the distance from radar to plane, 8km is the initial vertical altitude.

FD=time*24km/min

Using law of cosines

d=sqrt(FD^2+8^2-2*8*FD cos 110)
taking the derivative
d'= 1/2*1/sqrt ( ) * (2FD FD'-16cos110*FD')

d' is what you are looking for
FD' given as 24km/min, FD= 24*2=48km

so, it is plug and chug at this point.

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posted by bobpursley

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