Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 13 - Newton's Theory of Gravity - Exercises and Problems: 17

Answer

When the rocket is very far away from the earth, the rocket's speed is 9998 m/s

Work Step by Step

We can use conservation of energy to find the speed when the rocket is very far from the earth, where we can assume that the gravitational potential energy is zero. Let $M_e$ be the earth's mass and let $M_r$ be the rocket's mass. Let $R_0$ be the radius of the earth. $K_f+U_f = K_0+U_0$ $\frac{1}{2}M_r~v_f^2+0 = \frac{1}{2}M_r~v_0^2-\frac{G~M_e~M_r}{R_0}$ $v_f^2 = v_0^2-\frac{2~G~M_e}{R_0}$ $v_f = \sqrt{v_0^2-\frac{2~G~M_e}{R_0}}$ $v_f = \sqrt{(15,000~m/s)^2-\frac{(2)(6.67\times 10^{-11}~m^3/kg~s^2)(5.98\times 10^{24}~kg)}{6.38\times 10^6~m}}$ $v_f = 9998~m/s$ When the rocket is very far away from the earth, the rocket's speed is 9998 m/s.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.