A skier of mass 60kg starts at rest at the top of a steep slope with an incline of θ _s = 40°. The slope has slight coefficient of friction μ _k = 0.05. The slope is L = 100 meters long. At the bottom of the slope, there is an ice ramp (frictionless) that is 10 meter long and angled up θ _r = 30°.

• Draw a diagram of the problem.
• How much potential energy does the skier start with?
• How much total energy does the skier start with?
• How much energy is lost to friction on the slope?
• How fast is the skier travelling when she flies off the ramp?
• If there is a large trampoline positioned to catch the skier at the same altitude (y-position) as the beginning of the ramp, where should it be positioned?
• The trampoline behaves like a spring. If the first bounce on the trampoline depresses the trampoline surface by Δy = 1 meter. Without worrying about energy losses. What is the characteristic spring constant of the trampoline?
• Due to losses in the system, the trampoline losses about 2000 Joules every bounce. How many times does the skier bounce?

Where does 2000 joules on each bounce go? Speculate.