Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 13 - Newton's Theory of Gravity - Exercises and Problems: 14

Answer

When the rocket is very far away from the earth, the rocket's speed is 10,000 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. $K_f+U_f = K_0+U_0$ $\frac{1}{2}M_r~v_f^2+0 = \frac{1}{2}M_r~v_0^2-\frac{G~M_e~M_r}{R_0}$ $v_f^2 = v_0^2-\frac{2~G~M_e}{R_0}$ $v_f = \sqrt{v_0^2-\frac{2~G~M_e}{R_0}}$ $v_f = \sqrt{(15,000~m/s)^2-\frac{(2)(6.67\times 10^{-11}~m^3/kg~s^2)(5.98\times 10^{24}~kg}{6.38\times 10^6~m}}$ $v_f = 10,000~m/s$ When the rocket is very far away from the earth, the rocket's speed is 10,000 m/s.
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