Hi there,

Would anyone be able to tell me if I'm doing this problem correctly? Any help/pointers will be greatly appreciated. Thanks! Ana

A plane flying with a constant speed of 29 km/min passes over a ground radar station at an altitude of 16 km and climbs at an angle of 45 degrees. At what rate is the distance from the plane to the radar station increasing 5 minutes later?

x = 29 cos(45°)t = 20.5t

y = 29 sin(45°)t = 20.5t

Overall distance from radar station at any given time t =

d = sqrt(x^2 + (y + 16)^2)

= sqrt(420.5t^2 + 420.5t^2 + 656t + 256)

= (841t^2 + 656t + 256)^(1/2)

d(d/dt) = (1/2)(841t^2 + 656t + 256)^(-1/2)(1682t + 656)

for t = 5, answer = 28.924 km/min