Physics question: Conservation of Energy?

Question

Athlete will sprint 100 m, starting from rest, then leap onto a 20 kg bobsled. The person and bobsled will then slide down a 50 m long ice-covered ramp, sloped at 20 degrees, and into a spring with a carefully calibrated spring constant of 2000 N/m. The athlete who compresses the spring the farthest wins the gold medal. Lisa, whose mass is 40 kg, has been training for this event. She can reach a max. speed of 12 m/s in the
100 m dash.
(a) How far will Lisa compress the spring?
(b) The Olympic Commitee has very exact specifications about slope and angle of ramp. Is this necessary? If the committee asks your opinion, what factors about the ramp will you tell them are important?

Answer 1

Assuming no friction or air resistance, E = PE + KE = mgh + 0.5*m*v^2 = 40*9.81*50*sin(20deg) + 0.5*40*12^2
Compressing the spring, E = 0.5*k*x^2, so x=sqrt(2*E/k) (answer a)
For answer b, first I'd tell the IOC that the whole thing is unfair since a heavier athlete can equal the energy of a lighter opponent by just walking onto the bobsled. (Then they'll never ask for your opinion again!) I don't understand your reference to angle and slope; aren't they attributes of the same thing? Maybe you're saying the IOC specifies both the angle and the slope; this would be redundant. Anyway, if no friction or air resistance were assumed, which actually would be significantly erroneous, you'd tell them that the slope is irrelevant and only the drop matters.