Explanation Given information: A skydiver weigh w = 192 pounds if k = 1.2 lb − s / ft . Mass and weight are related by w = m g . v ' = − ( k g w ) ( v + w k ) with g = 32 ft / s 2 . His initial velocity is zero. Formula used: Terminal velocity is − m g k , where m is mass, w is weight and k is air resistance constant. The general solution of the equation of form v ' = − ( k m ) ( v + m g k ) is v ( t ) = − m g k + C e − ( k m ) t . Calculation: From the given information, we have w = 192 pounds k = 1.2 l b − s / ft g = 32 ft / s 2 v ( 0 ) = 0 v ' = − ( k g w ) ( v + w k ) (Given) The general solution for the above equation is v ( t ) = − w k + C e − ( k g w ) t . v ( t ) = − 192 1.2 + C e − ( ( 1.2 ) ( 32 ) 192 ) t v ( t ) = − 160 + C e − ( 0.2 ) t Using the condition v ( 0 ) = 0 in above equation, we get 0 = − 160 + C e 0 ⇒ C = 160 Substituting C = 160 in v ( t ) = − 160 + C e − ( 0

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 10.2, Problem 14E

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To find:The terminal velocity of a skydiver and the time taken for him to reach half of his terminal velocity.

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Chapter 10.2, Problem 13E

Chapter 10.2, Problem 15E

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The terminal velocity of a skydiver and the time taken for him to reach half of his terminal velocity.

Solution Summary: The author calculates the terminal velocity of a skydiver and the time taken for him to reach half of his velocity.

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To find:The terminal velocity of a skydiver and the time taken for him to reach half of his terminal velocity.

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Chapter 10 Solutions