How Do You Calculate the Stopping Time and Displacement of a Skier on a Slope?

[sonoftunk]

Homework Statement

A young skier (25kg) pushes off with ski poles to give herself an initial velocity of 3.5 m/s down a hill with 5^o slope with a coefficient of friction of 0.20.
Find the time until skier comes to stop and her displacement.
Therefore
m = 25kg
v_i = 3.5m/s
$$\theta$$ = 5^o
$$\mu$$ = 0.20

Homework Equations

All kinematic-based equations
Newton's Laws (specifically $$\stackrel{\rightarrow}{F}$$ = m($$\Delta$$$$\stackrel{\rightarrow}{v}/$$$$\Delta$$t)
F_F = $$\mu$$F_N

The Attempt at a Solution

My idea for this was to find the F_NET and sub that into Newton's Second Law, solving for $$\Delta$$t (assuming that $$\stackrel{\rightarrow}{v}$$_f is zero)
My solution for $$\Delta$$t was 1.3 seconds, correct to two significant digits (to me, that seems quite off)

For the second half of the question, finding the distance, I used $$\Delta$$$$\stackrel{\rightarrow}{d}$$ = $$\stackrel{\rightarrow}{v}$$_i + $$\frac{1}{2}$$$$\stackrel{\rightarrow}{a}$$($$\Delta$$t)² using $$\stackrel{\rightarrow}{a}$$ as the component force of gravity acting parallel to the hill and I got 23m, correct to 2 significant digits.

I was then told I completed the question completely wrong. Now I'm lost. What was I supposed to do?

 

[LowlyPion]

Welcome to PF.

Maybe consider it is a Kinetic Energy to work from friction problem?

Work would be the (μ*mg*cos5° - mg*sin5°) times the distance and that would equal the KE.

 

[sonoftunk]

I haven't learned kinetic energy yet...

BTW, this is a correspondence coarse for Grade 12 Physics in Ontario..

 

[buffordboy23]

You know the frictional force, so find the net acceleration on the skier due to friction and gravity.