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Skier on slope

A skier traveling at 31.3 m/s encounters a 25.9 degree slope. If you could ignore friction, to the nearest meter, how far up the hill does he go? 114 meters

But...If the coefficient of kinetic friction in the previous problem was actually 0.07 and the slope 30 degrees, to the nearest meter how far up the hill does he go?

Solution Preview

Both questions can be addressed via the law of conservation of energy, but first let us set notations:

starting speed v_0 = 31.3 m/s
slope angle A_1 = 25.9° in the 1st question
and A_2 = 30° in the 2nd question
skiier mass m - its value is not needed, but it is customary and convenient to write equations with it
coefficient of friction: k_1 = 0 in the 1st question and k_2 = 0.07 in the 2nd question
force of friction F
normal force N
free fall acceleration g

the hight of the upper point on the ...