Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 6 - Work and Energy - Problems: 32

Answer

1.3 m.

Work Step by Step

Jane’s mechanical energy is conserved. Take y = 0 at the bottom. The initial KE + initial PE equals the final KE + final PE. She comes to a momentary stop at the end. $$\frac{1}{2}mv_i^2 + mgy_i=\frac{1}{2}mv_f^2 + mgy_f $$ $$\frac{1}{2}mv_i^2 + 0 = 0 + mgy_f $$ $$y_f=\frac{v_i^2}{2g}=1.3 m$$ The vine length does not matter as long as it is longer than about 0.65 m so that she can rise 1.3 m.
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