The distance between you and the plane is increasing by __ mph.

Question

An experimental plane, currently overhead, is flying at 120 mph at an altitude of 32 thousand feet. How fast is the plane’s distance from you increasing at the moment when the plane is flying over a point on the ground 24 thousand feet from you?

Answer 1

120 mph = 120 x 5280 / 3600 ft/s = 176 ft/s

So if time starts now, after t seconds distance from you is d when

d^2 = (32000 ^2 + (176t)^2 )

So 2d dd/dt = 2 x 176^2 x t

When the plane is flying over the ground 24000 ft from you

d = √ (32000 ^ 2 + 24000 ^ 2) = 40000 ft

t = 24000 / 176

giving dd/dt = 105.6 ft/s