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A snowboarder of mass 82.0 kg (including the snowboard's mass) slides straight down a "double black diamond" hill. The hill is 45 metres in length and inclined at 40° below the horizontal. The coefficient of kinetic friction between the snow and snowboard. A snowboarder of mass 82.0 kg (including the snowboard's mass) slides straight down a "double black diamond" hill. The hill is 45 metres in length and inclined at 40° below the horizontal. The coefficient of kinetic friction between the snow and snowboard is 0.21.

(i) Determine the work done by the force of gravity.

(ii) Determine the work done by the normal force.

(iii) Determine the work done by the force of friction.

(iv) If the hill were less steep, but the distance down the hill remained constant, describe (qualitatively) how the above quantities would change.

(v) Use the Work-Energy Theorem to compute the snowboarder's maximum speed.

(vi) Use Conservation of Mechanical Energy to compute the snowboarder's maximum speed.

(vii) Which of the maximum speeds computed in (v) and (vi) is correct, and why?

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