University Physics with Modern Physics (14th Edition)

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

Chapter 8 - Momentum, Impulse, and Collision - Problems - Exercises - Page 264: 8.11

Answer

(a) $A = 500~N/s^2$ (b) The rocket exerts an impulse of 5810 kg m/s. (c) The velocity changes by 2.70 m/s.

Work Step by Step

(a) When t = 1.25 s: $At^2 = 781.25~N$ $A = \frac{781.25~N}{t^2}$ $A = \frac{781.25~N}{(1.25~s)^2}$ $A = 500~N/s^2$ (b) $J = \int_{2.00}^{3.50}F~dt$ $J = \int_{2.00}^{3.50}At^2~dt$ $J = \frac{A}{3}t^3\vert_{2.00}^{3.50}$ $J = \frac{(500~N/s^2)}{3}[(3.50~s)^3 - (2.00~s)^3]$ $J = 5810~kg~m/s$ The rocket exerts an impulse of 5810 kg m/s. (c) $\Delta p = J$ $m \Delta v = J$ $\Delta v = \frac{J}{m} = \frac{5810~kg~m/s}{2150~kg}$ $\Delta v = 2.70~m/s$ The velocity changes by 2.70 m/s.
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