Explanation Concept used: Universal law of gravitation: F = G m 1 m 2 r 2 The work-energy theorem is W = 1 2 m v 2 Calculation: The works required to increase the separation between two masses M and m from r 1 to r 2 is, Therefore, the work performed when the train reaches the end of 3m long electric track is, W = G M m ( 1 r 1 − 1 r 2 ) Here, M and r 1 is mass and radius of the earth. Let m is mass of the rocket. Then r 2 = ( r 1 + 20000 ) m { r = 20 k m } , And W = G M m ( 1 r 1 − 1 r 1 + 20000 ) If a rocket is launched with an initial velocity v 0 then the initial kinetic energy is K . E = 1 2 m v 2 2 . When the rocket reaches the maximum height, the velocity is zero. Therefore, the kinetic energy decrease from 1 2 m v 2 2 to 0 Then by work-energy theorem, W = 1 2 m v 0 2 G M m ( 1 r 1 − 1 r 1 + r )

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ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 6.5, Problem 42E

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what initial velocity v0 must be fire a rocket so that it attains at the maximum height of 20km above the earth.

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Chapter 6.5, Problem 41E

Chapter 6.5, Problem 43E

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Chapter 6 Solutions

Calculus: Early Transcendentals

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what initial velocity v 0 must be fire a rocket so that it attains at the maximum height of 20 k m above the earth.

Solution Summary: The author explains the work-energy theorem for determining the initial velocity of a rocket.

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what initial velocity v0 must be fire a rocket so that it attains at the maximum height of 20km above the earth.

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Chapter 6 Solutions

what initial velocity v 0 must be fire a rocket so that it attains at the maximum height of 20 k m above the earth.

Solution Summary: The author explains the work-energy theorem for determining the initial velocity of a rocket.

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To evaluate: what initial velocity v0 must be fire a rocket so that it attains at the maximum height of 20km above the earth.

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Chapter 6 Solutions

To evaluate:

what initial velocity v0 must be fire a rocket so that it attains at the maximum height of 20km above the earth.