To determine To calculate: The rate of change of the distance between air traffic controller and aircraft with respect to time that that is the derivative of d z d t . Explanation Given: The provided conditions are y = 5 miles , z = 13 miles and d x d t = 325 mph . Formula used: Chain Rule: If f and g are functions and y = [ g ( x ) ] , then y ′ = f ′ [ g ( x ) ] ⋅ g ′ ( x ) provided that f ′ [ g ( x ) ] and g ′ ( x ) exists. Calculation: Draw position diagram: In above diagram, consider z be the distance between traffic controller and aircraft, y be the height of aircraft. Apply Pythagoras theorem to write relationship between x and z . x 2 + ( 5 miles ) 2 = z 2 …...…... (1) Calculate the value of x corresponding to z = 13 miles . Substitute 13 miles for z in equation (1): x 2 + ( 5 miles ) 2 = ( 13 miles ) 2 x 2 = ( 13 miles ) 2 − ( 5 miles ) 2 x 2 = 144 miles 2 Take square root: x = 144 miles 2 = ( 12 miles ) ( 12 miles ) = ( 12 miles ) 2 = ± 12 miles Here, distance between traffic controller and aircraft will never negative

12th Edition

ISBN: 9780135240687

Author: Lial

Publisher: PEARSON

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Chapter 12.5, Problem 28E

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To calculate: The rate of change of the distance between air traffic controller and aircraft with respect to time that that is the derivative of dzdt.

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Chapter 12.5, Problem 27E

Chapter 12.5, Problem 29E

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