## Fundamentals of Physics Extended (10th Edition)

Published by Wiley

# Chapter 8 - Potential Energy and Conservation of Energy - Problems: 22a

#### Answer

$h=H\sin ^{2}\theta =20m\times \sin ^{2}\left( 28^{0}\right) \approx 4,41m$

#### Work Step by Step

Lets calculate total energy of skier relative to end of ramp (initial kinetic energy of skier is zero since it started with zero speed) $E_{tot}=E_{k}+E_{p}=0+mgH=mgH(1)$ At the end of the ramp the potential energy of skier will be zero ( becouse it will be at the same height with end of ramp) so it will only have kinetik energy $E_{tot}=E_{k}+E_{p}=E_{k_{1}}+0=E_{k_{1}}\left( 2\right)$ and also we can write: $E_{k_{1}}=\dfrac {mv^{2}_{1}}{2}\left( 3\right)$ $v_{1}$ is the speed at the end of the ramp. So from (1),(2) and (3) we get $\dfrac {mv^{2}_{1}}{2}=mgH\Rightarrow v_{1}=\sqrt {2gH}(4)$ So lets calculate maximum height can skier go: $h=\dfrac {v^{2}_{0}\sin ^{2}\theta }{2g}\left( 5\right)$ So from (4) and (5) we get: $h=H\sin ^{2}\theta =20m\times \sin ^{2}\left( 28^{0}\right) \approx 4,41m$

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