A skier starts from rest at the top of a 50 m hill, skis down a 36° incline into a valley, and continues up a 30 m high hill. Both hill heights are measured from the valley floor. Assume that you can neglect friction and the effect of ski poles.
(a) How fast is the skier moving at the bottom of the valley?
______m/s
(b) What is the skier's speed at the top of the next hill?
_____m/s
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Verified answer
Initially, E = Ep = mgh = M * 9.8m/s² * 50m = M * 490 m²/s²
a) At the bottom of the valley, Ep = 0 and Ek = ½Mv² = M * 490m²/s²
m cancels:
v = 31.3 m/s
b) The potential energy given up is equal to the kinetic energy.
Mg(50m - 30m) = ½Mv²
M cancels;
v = √(2 * 9.8m/s² * 20m) = 19.8 m/s