Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 5 - Force and Motion-I - Problems - Page 118: 31a

Answer

$1.18$ meters

Work Step by Step

Ref to the attached figure....the Free Body Diagram. g = accl due to gravity. Acceleration along the incline acting against the motion is $a = -g * sin \theta$ When it stops, the speed $v$ = 0. t = time to stop. Using $v = v_{0} + at$, we get $t = - v_{0}/a$. now $\Delta x$ = distance traveled by the block on the incline = $v_{0}t + \frac{1}{2}at^{2}$. Replace $t = - v_{0}/a$. we get $\Delta x$ = $v_{0} * (- v_{0}/a) + \frac{1}{2}a(- v_{0}/a)^{2}$ = $-\frac{1}{2} (v_{0}^{2}/a)$ = $\frac{-\frac{1}{2} * (3.5)^{2}} {(9.8) * sin 32^{\circ}}$ = $1.18$ meters
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