How Does Physics Apply in the New Olympic Sled and Spring Event?

[Ajmathusek]

In a new Olympic event athletes run as fast as they can,
jump onto a sled, ride it down a hill and compress a
spring as far as they possibly can. (who thinks of these
any ways)
a. Consider a 55.0 kg athlete that makes it to a top
speed of 12.5 m/s before jumping onto a 15.0 kg sled. What is the athlete/sled initial speed as
she starts down the hill?
b. If the hill is 25.0 m long at an angle of 15.0 0 how much mechanical energy does the athlete/sled
initially have?
c. If the hill has a coefficient of friction of 0.125, what is the speed she reaches at the bottom of
the hill, just before hitting the spring?
d. Assuming the spring is located just at the bottom, and the coefficient of friction is the same as
on the hill, how far could this athlete compress the spring if it has a coefficient of 1250 N/m?

I am not sure how to go about this question. I know that you need acceleration for initial speed but can't figure out how to find it with the numbers given.

 

[mfb]

You don't need an acceleration. This is just a "collision" between athlete and sled. Only in (d), you can (but do not have to) calculate an acceleration.

 

[Ajmathusek]

So how do I go about doing it?

 

[mfb]

With the formulas you know for collision processes...

After the collision with the sled both move with the same velocity. Is this an elastic or inelastic collision?