Chapter 13.4, Problem 46E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

A rocket burning its onboard fuel while moving through space has velocity **v**(*t*) and mass *m*(*t*) at time *t*. If the exhaust gases escape with velocity **v*** _{e}* relative to the rocket, it can be deduced from Newton’s Second Law of Motion that

(a) Show that

(b) For the rocket to accelerate in a straight line from rest to twice the speed of its own exhaust gases, what fraction of its initial mass would the rocket have to bum as fuel?

**(a)**

To determine

**To show:** The vector

Explanation

**Given data:**

Rearrange the equation (1).

Take integration with respect to *t* on both sides.

**(b)**

To determine

**To find:** The fraction of its initial mass would have to burn the rocket as fuel.

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