## Physics: Principles with Applications (7th Edition)

Published by Pearson

# Chapter 6 - Work and Energy - Problems: 31

45.4 m/s.

#### Work Step by Step

The skier’s mechanical energy is conserved. Take y = 0 at the bottom of the hill. The initial KE + initial PE equals the final KE + final PE. $$\frac{1}{2}mv_i^2 + mgy_i=\frac{1}{2}mv_f^2 + mgy_f$$ $$0 + mg(105 m)=\frac{1}{2}mv_f^2 + 0$$ The mass cancels out. Solve for the final speed. $$v_f=\sqrt{2gy_i}=45.4 m/s$$

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