# A girl and her bicycle have a total mass of 35 kg. At the top of a hill her speed is5 m/s. The hill is 11 m high and 100 m long. If the force of frictionas she rides down the hill is 15 N,what is her speed at the bottom?

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Whoever wrote that is very wrong. You need to considerthe total energy she has. At the top she has both KE and PE. Her KE is $$\displaystyle{\frac{{{1}}}{{{2}}}}{m}{v}^{{2}}$$ or $$\displaystyle\frac{{\frac{{{1}}}{{{2}}}}}{{{35}}}{\left({5}\right)}^{{2}}$$ Plus her PE given amgh or $$\displaystyle{35}\times{9.8}\times{11}$$. She loses energy on the way down due tofriction in the amount of $$\displaystyle{F}\times{D}$$ or $$\displaystyle{15}\times{100}={1500}$$. So to find V final. ADD the KE top plus the PE top and subtract 1500 and that equals $$\displaystyle{\frac{{{1}}}{{{2}}}}{m}{v}^{{2}}$$ (KE only at bottom) You should get 12.4 m/s