(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A skier starts from rest on a 20m high, 20° slope. μ_{k}=0.210

Find the horizontal distance traveled by the skier.

From this, for the equations below we know that:

y_{f}= 0

v_{i}= 0

v_{f}= 0

2. Relevant equations

W_{net}= W_{nc}+ W_{g}= ΔKE

W_{net}= -f_{k}d

W_{nc}= ΔKE + ΔPE

W_{nc}= ΔKE + mg(y_{f}- y_{i})

KE = 1/2mv^{2}

PE = mgy

f_{k}= μ_{k}mg

3. The attempt at a solution

So I went with the work of a non-conservative force

W_{nc}= (KE_{f}- KE_{i}) + (PE_{f}- PE_{i})

W_{nc}= (1/2mv_{f}^{2}- 1/2mv_{i}^{2}) + (mgy_{f}- mgy_{i})

From given, I eliminated all 0 quantities, leaving me with

W_{nc}= -mgy_{i}

Then plugged in W_{net}= -f_{k}d = -μ_{k}mgd so,

-μ_{k}mgd = -mgy_{i}

eliminated like terms (m, g):

-μ_{k}d = -y_{i}

and solved for d

d = y_{i}/μ_{k}

and plugged in the knowns

d = 20m/0.210

d = 95.2m

I realize this is the distance traveled from the top of the hill to the end of motion, but all they want is the horizontal distance, so now I have to solve for the distance traveled from the top of the hill to the bottom of the hill. The only thing I think that changes between the above work and the distance from the top to bottom is the final velocity which will be nonzero.

So my question is, how do I find the distance traveled from the top of the hill to the bottom?

Or am I going about this wrong? Is there a more direct way to find just the horizontal distance traveled?

Oh I should add, the answer given by the book is 40.3m

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# Work done by friction on a skier and resulting distance the skier travels

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