(a)

Write  as a function of .

If the altitude is .

Observe the figure:

.

.

(b)

The speed of plane is .

.

Find .

Apply derivative on each side with respect to .

Derivative of inverse trigonometric functions: .

.

Find the value of  when :

Substitute  and  in .

.

.

Find the value of  when :

Substitute  and  in .

.

If the altitude of the plane were changed to , the rate of change of  would be slower while the plane was further away from the man but then faster as it got closer.

(a) .

(b) When ,  ; when , .

If the altitude of the plane were changed to , the rate of change of  would be slower while the plane was further away from the man but then faster as it got closer.