Kinetics Questions

Question

A snowboarder takes speed downhill in order to get up a hill without

pushing. If he arrives at the bottom of the hill with a velocity of 60 km/h,

will he be able to get up a hill 75 m long with an 8% slope? (Kinetic

friction coefficient: snowboard-snow = 0.1 and air resistance is

neglected). (Hint: a 1% slope rises 1 m vertically for every 100 m of

lateral travel.)

Answer 1

This is an energy problem. We need to find the energy that the snowboarder will require to make it up the hill. This energy has two parts:

1. change in altitude: E_1 = m*g*h = m*(9.8 m/s^2)*75m*0.08 = 58.8*m.
2. frictional loss: The normal force that the slope exerts on the snowboarder is m*g*cos(theta), where theta = arctan(0.08). The energy loss is the frictional work done by the snowboarder on the slope: E_2 = 0.1*m*g*cos(theta)*75m = 73.27*m.

Now, what is the kinetic energy of the snowboarder before approaching the hill?

E_0 = 0.5*m*v^2 = 0.5*m*(60000/3600 m/s)^2 = 138.89*m > E_1+E_2.

So, the answer is yes. He will make it up, but just barely.