# Math Help - Urgent help on related rates:

1. ## Urgent help on related rates:

An airplane flies at a height of 9km in the direction of an observer on the ground at a speed of 800kph. Find the rate of change of the angle of elevation of the plane from the observer at the instant when the angle is \pi over 4 radians.
Ill be the one to differentiate this:

2. Originally Posted by ^_^Engineer_Adam^_^
An airplane flies at a height of 9km in the direction of an observer on the ground at a speed of 800kph. Find the rate of change of the angle of elevation of the plane from the observer at the instant when the angle is \pi over 4 radians.
Ill be the one to differentiate this:
Assume a flat Earth, then the angle of elevation phi satisfies:

tan(phi) = height/range ... (1)

height = 9000 m.

d range/dt = 800000*60*60 m/s.

When the elevation is pi/4 rad, the range is 9000 m.

Use implicit differentiation on (1), and plug in what you know to find d phi/dt.

RonL