A 80kg skier, starting from rest, reaches a speed of 100 km/h after covering a d

Question

A 80kg skier, starting from rest, reaches a speed of 100 km/h after covering a difference in altitude of 50m, and traveling a distance of 400m. Calculate the average force exerted by the skier's muscles - propelling himself by pushing the sticks against the ground - assuming that friction between skis and the snow together with air resistance exert a force of 50N on the skier opposite to its direction of motion.

My teacher started us off by giving us: ki + ui + wair + wpush = kf + uf, and I know that ki and uf are both zero, due to the velocity being zero, and that the skier isn't moving in the final position, and therefore has no height, respectively. I know that ui is (80kg)(9.81 m/s2)(50m), but I don't know how to do the wair. If you could explain it to me, that would be great.

Explanation / Answer

potential energy of the skier at height of 50 m is:

Ui = m g h = 80 x 9.81 x 50 = 39,240 J

the work done by resistive force is:

W = 50 x 400 = 20,000 J

Kinetic energy of skier is:(its after)

KEf = 1/2 m v^2 = 0.5 x 80 x 27.78^2 = 30869.14 J

from the conservation of mechanical energy

Ui + Ki + W(push) + W(resist) = KEf

39240 + 0 + W(push) -20000 = 30869.14

W(push) = 11629.136

so the pushing force exeretd for the entire 400 m is:

F(push) = 11629.136/400 = 29.03 N

Hence, F(push) = 29.03 N

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