Predict the motion of a skier (with friction)

You have ALREADY done this calculation:

• height of ramp H = 50 m
• length of ramp (along the surface) L = 115 m

If the skier starts from rest at the top of the ramp, and slides without friction, how fast will he be moving when he leaves the ramp at the bottom?

However, in real life, skiers don't reach the bottom of the ramp with the theoretical speed. Instead, the actual speeds are closer to about v = 26 m/s.

Let's pretend that the only reason for this discrepancy is friction between the skis and the icy ramp. If that's the case, what is the coefficient of kinetic friction between the skis and the ice?

1. determine the ACTUAL acceleration of the skier
2. compute the force of friction on the skier
3. determine the coefficient of kinetic friction between skier and ramp

Fine. But ... is this correct? Compare your value to the coefficients of static friction we measured earlier between a metal track and a block covered with fabric.

1. Do you think that the coefficient of kinetic friction you just derived for ski-to-ice is reasonable?
2. If not, how can you explain the difference between theoretical and actual take-off speeds?