A plane is flying west at 500 ft/sec at an altitude of 4000 ft. The plane is tracked by a searchlight on the ground. If the light is to be trained on the plane, find the change in the angle of elevation of the searchlight at horizontal distance of 2000 ft.

Question

A plane is flying west at 500 ft/sec at an altitude of 4000 ft.  The plane is tracked by a searchlight on the ground.  If the light is to be trained on the plane, find the change in the angle of elevation of the searchlight at horizontal distance of 2000 ft.

bobpursley · Accepted Answer

tan(elevation)=4000/x
d/dx tanE =-4000/x^2 dx/dt
but d/dttanE= sec^2E * dE/dt
finally...

sec^2 E * dE/dt=-4000/x^2 dx/dt

solve for dE/dt when x=2000, You can figure secE from the triangle. You are given dx/dt as 500ft/sec