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

1. Feb 29, 2012

### Sequence1123

1. The problem statement, all variables and given/known data
A skier starts from rest on a 20m high, 20° slope. μk=0.210
Find the horizontal distance traveled by the skier.
From this, for the equations below we know that:
yf = 0
vi = 0
vf = 0

2. Relevant equations
Wnet = Wnc + Wg = ΔKE
Wnet = -fkd
Wnc = ΔKE + ΔPE
Wnc = ΔKE + mg(yf - yi)
KE = 1/2mv2
PE = mgy
fk = μkmg

3. The attempt at a solution
So I went with the work of a non-conservative force
Wnc = (KEf - KEi) + (PEf - PEi)
Wnc = (1/2mvf2 - 1/2mvi2) + (mgyf - mgyi)
From given, I eliminated all 0 quantities, leaving me with
Wnc = -mgyi
Then plugged in Wnet = -fkd = -μkmgd so,
kmgd = -mgyi
eliminated like terms (m, g):
kd = -yi
and solved for d
d = yik
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

2. Feb 29, 2012

### Staff: Mentor

Is this the full statement of the problem?

I'm guessing that after the skier gets to the bottom of the slope, she skis over a horizontal stretch of ground? Perhaps it's that horizontal distance that they want.

3. Feb 29, 2012

### Sequence1123

AH! I figured it out...

I had to find the length of the bottom of the triangle formed by the horizontal and the slope of the hill. sin20° = 20/x (where x is the hypotenuse, or the length of the slope of the hill)
from that I got x ≈ 58.5m
Then,
cos20° = x/58.5m (where x is the length of the bottom of the triangle)
x ≈ 54.9m
then subtract that from the total length traveled by the skier, 95.2m - 54.9m = 40.3m which is the answer given by the book.