# Skier on a Slope - Find Total Distance

1. Feb 27, 2010

### erok81

1. The problem statement, all variables and given/known data

Starting from rest, a 75 kg skier slides down a 17.0 º slope. If the coefficient of kinetic friction between the skis and snow is
0.120 and it takes 28.2 s to get to the bottom, how long is the ski trail?

2. Relevant equations

$$F = ma$$
$$s_f = s_i +v_i + 1/2at^2$$

3. The attempt at a solution

I drew a diagram and came up with this:

The acceleration of the skier down the slope is mgsin(17) the friction going the opposite direction is mgsin(17)0.120.

F_net is mgsin(17)-mgsin(17)0.120

Taking F=ma and solving for a I came up with F/m=a

So....[mgsin(17)-mgsin(17)0.120]/m

This gave me 2.52 m/s^2

Plugging that into one of my kinematic equations....

$$s_f = s_i +v_i + 1/2at^2$$

s=(.5)(2.52)(28.2^2)

I ended up with the final distance as 1002m.

What am I missing?

2. Feb 27, 2010

### shallgren

Remember that the normal (for dealing with the friction) is going to involve cosine, not sine.

3. Feb 27, 2010

### erok81

Duh.

Yep, that was it.

Thank you.