Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 5 - Section 5.2 - Multiple Objects - Example - Page 75: 5.4

Answer

12 seconds

Work Step by Step

We know the x-component of the rock's force as well as the equation for the y-component of the climber: Climber y: $F_t - mg = -ma $ Rock: x: $F_t = m_{rock}a$ We plug the value for $F_t$ into the climber equation to find: $m_{rock}a- mg = -ma \\ mg = m_{rock}a + ma \\ a = \frac{mg}{m+m_{rock}} =\frac{ (73 \times 9.81)}{73+940}=.71 \ m/s^2$ Using this, we find t: $t = \sqrt{\frac{2x}{a}}=\sqrt{\frac{2\times 51}{.71}}=12s$
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