Explanation Given information: Weight of skydiver = 192 lb Formula used: Differential equation for velocity is given as v ' = − ( k g w ) [ v + w k ] Solve the above linear differential equation to obtain solution as v ( t ) = − w k + C e − ( k g w ) t ........ ( 1 ) Terminal velocity is obtained by lim t → ∞ v ( t ) = − w k Calculation: Here, w = 192 lb and k = 1.2 l b − sec / f t Hence terminal velocity is lim t → ∞ v ( t ) = − w k = − 192 1.2 = − 160 Thus terminal velocity is − 160 ft/sec [ terminal velocity = − 160 ft/sec ] Next to find the time it will take to reach half of his terminal velocity, if his initial velocity is zero. Therefore, v ( 0 ) = 0 put in ( 1 ) to find C

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 9.2, Problem 14E

To determine

The terminal velocity of a skydiver of weight w=192 pounds if k=1.2 lb−s/ft. The time does it take him to reach half of his terminal velocity if his initial velocity is zero.

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Chapter 9.2, Problem 13E

Chapter 9.2, Problem 15E

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Calculus: Early Transcendentals

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The terminal velocity of a skydiver of weight w = 192 pounds if k = 1.2 lb − s/ft . The time does it take him to reach half of his terminal velocity if his initial velocity is zero.

Solution Summary: The author calculates the terminal velocity of a skydiver of weight w=192 pounds if his initial velocity is zero.

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The terminal velocity of a skydiver of weight w=192 pounds if k=1.2 lb−s/ft. The time does it take him to reach half of his terminal velocity if his initial velocity is zero.

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Chapter 9 Solutions