Solve for Length of Friction-Ridden Ice Patch | Work-Energy Theorem Hint

[kingsean]

I've been working on a problem and I'm stumped :| I'm usually pretty good at deriving the equations for problems and solving them once I find out what I need to be solved. But this one is a bit too ambiguous for me, and I'm looking for a few hints :) Anything is appreciated!

On an essentially friction-less, horizontal ice rink, a skater moving at 3.0m/s encounters a rough patch that reduces her speed by 45% due to a friction force that is 25% of her weight. Use the work-energy theorem to find the length of this rough patch.


I've tried a few methods but, alas, no answer. The back of the book says 1.5m if that is of any assistance.

Thanks again!

 

[dav2008]

Just solve the problem using "m" for the mass and it should cancel out in the end.

You know the initial energy will just be the kinetic energy (K) and that will equal the final kinetic energy plus work done by friction ( K+W_f )

 

[kingsean]

Just solve the problem using "m" for the mass and it should cancel out in the end.

You know the initial energy will just be the kinetic energy (K) and that will equal the final kinetic energy plus work done by friction ( K+W_f )

I've taken this into consideration, but my answers still end up being too high or too low :(

 

[dav2008]

I worked it out and got 1.46 meters as the answer.

I said that the final velocity was 3*.45 (although the wording would suggest that it should be 3-(3+.45) but that gives me 1.28)

Can you show how you're doing it and what answer you get?