a. Explanation Given information: A 1-kg ball is launched upwards at 30 m/s is acted on by gravity and air resistance. Formula used: 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 . Proof: From the given information, we have m = 1 k g v ( 0 ) = 30 g = 9.8 We also have the velocity as v ( t ) = − m g k + C e − ( k m ) t . Using v ( 0 ) = 30 in above equation, we have 30 = − m g k + C e 0 30 = − ( 1 ) ( 9.8 ) k + C ( 1 ) ⇒ C = 30 + 9.8 k Substituting C = 30 + 9.8 k in v ( t ) = − m g k + C e − ( k m ) t , we get v ( t ) = − m g k + ( 30 + 9.8 k ) e − ( k m ) t (1) The ball’s velocity is zero at time is denoted by v ( t * ) = 0 Using this in (1), we get 0 = − m g k + ( 30 + 9 b. To determine To prove : y ( t * ) = 30 k − 9.8 ln ( 150 k 49 + 1 ) k 2

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 10.2, Problem 17E

To determine

To prove:The ball’s velocity is zero at time t*=1kln(30k9.8+1)

To determine

To prove: y(t*)=30k−9.8ln( 150k 49+1)k2

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Chapter 10.2, Problem 16E

Chapter 10.2, Problem 18E

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To prove: The ball’s velocity is zero at time t * = 1 k ln ( 30 k 9.8 + 1 )

Solution Summary: The author explains that the ball's velocity is zero at time. The general solution of the equation is v'=-raisebox1exmg!