(a)

Write as a function of .

If the altitude is .

Observe the figure:

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(b)

The speed of plane is .

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Find .

Apply derivative on each side with respect to .

Derivative of inverse trigonometric functions: .

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Find the value of when :

Substitute and in .

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Find the value of when :

Substitute and in .

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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.