University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 13 - Gravitation - Problems - Exercises - Page 426: 13.25

Answer

(a) The orbital speed is 4.1 m/s. Since this is not a fast speed for a baseball, it would be possible to throw the ball at this speed. (b) It would take 2.6 hours for the ball to make one orbit so that the batter could actually try to hit the ball. We would definitely not describe this baseball game as action-packed.

Work Step by Step

(a) We can find the orbital speed of the ball. $v = \sqrt{\frac{G~M}{R}}$ $v = \sqrt{\frac{(6.67\times 10^{-11}~m^3/kg~s^2)(1.5\times 10^{15}~kg)}{6.0\times 10^3~m}}$ $v = 4.1~m/s$ The orbital speed is 4.1 m/s. Since this is not a fast speed for a baseball, it would be possible to throw the ball at this speed. (b) We can find the time of one orbit. $T = \frac{distance}{speed}$ $T = \frac{2\pi~R}{v}$ $T = \frac{(2\pi)(6.0\times 10^3~m)}{4.1~m/s}$ $T = 9195~s = 2.6~hours$ It would take 2.6 hours for the ball to make one orbit so that the batter could actually try to hit the ball. We would definitely not describe this baseball game as action-packed.
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