A skier is traveling on a horizontal 0deg. slope which has no resistance, at a rate of 3 m/s. She goes down a 10deg. slope, at the bottom she is going 15 m/s. 1) How long is the slope? Can I just get hints towards what formulas I need to be using here..

You're going to want to be using the conservation of energy for this. Assume that all of the skiier's gravitational energy is converted to kinetic energy. That will give you the height of the hill, then you'll want to use some trigonometry to find the length of the slope.

but you don't know the mass and not even the height, so how can you use conservation of energy. you said gravitational energy \[g= GM \div r ^{2}\] or if you meant to say potential energy, \[P.E. = mgh\] more help pls

oh, yeah my bad, I meant to say gravitational potential energy, \[E_k + E_p = E_{total}\]\[\frac{1}{2}mv_1^2+mgh_i = \frac{1}{2}mv_2^2+mgh_f\] the m's cancel out

also, if you assume that the final height is 0, then you can solve that for the initial height, and use trigonometry to find the length of the slope: \[sin \theta = \frac{h}{l}\]

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