Calculus Word Problem help?

Question

A highway patrol plane flies 3 mi above a level, straight road at a steady 120 mi/h. The pilot sees an oncoming car and with radar determines that at the instant the line-of-sight distance from plane to car is 5 mi the line-of-sight distance is decreasing at the rate of 160 mi/h. Determine the car’s speed along the highway.

Answer 1

We can draw a picture with a plane 3 miles high at point A, a perpendicular to the road at point B. At point C on the road, which is 5 miles LOS, is a car moving at an unknown speed towards the plane. The LOS is a hypotenuse from C to A. In a small time period, dt, the plane will move 120 dt. The car will move at vc dt. The LOS will decrease, but at the instant the points ABC are defined above, it is -160 mi/hr

The related rate is based on the triangle, for which
LOS^2 = 3^2 + [BC]^2. From the geometry, [BC]= 4 miles. In general, h^2+d^2= LOS^2, and
2h dh/dt + 2d dd/dt = 2LOS d(LOS)/dt.
dh/dt=0 if the plane flies at 3 miles high.
Then d dd/dt = LOS d(LOS)/dt
From our condition, 4 dd/dt = 5 * -160mph and dd/dt= - 200 mph. Since the plane contributes 120 mph to dd/dt, the car is approaching at 80 mph.

Answer 2

Seriously, you better go to school for that.