Final answer:
The problem involves conservation of momentum to find the combined velocity of a person and sled after collision, and then uses the concept of kinetic friction to calculate the coefficient of friction based on the distance traveled before coming to rest.
Step-by-step explanation:
The question can be addressed by applying the principles of conservation of momentum and the concept of kinetic friction. Since friction is to be ignored during the collision in part (a), we are dealing solely with a conservative momentum collision. Afterward, in part (b), we deal with nonconservative forces due to kinetic friction, which causes the sled-person system to come to rest.
To find the velocity of the sled and person after the jump (a), we set the initial total momentum equal to the final total momentum:
mpersonvperson = (mperson + msled)vfinal
58.4 kg * 3.86 m/s = (58.4 kg + 12.8 kg) * vfinal
Solving for final we get:
vfinal = (58.4 kg * 3.86 m/s) / (58.4 kg + 12.8 kg)
The resulting velocity will be the shared velocity of the sled and person as they move away after the collision.
For part (b), the coefficient of kinetic friction (μk) is found by using the work-energy principle, where the work done by friction is equal to the change in kinetic energy. The formula used is:
ffriction = μk * N
And the work done by friction (W) is:
W = ffriction * d
Since the sled comes to rest, the initial kinetic energy is entirely dissipated by friction, which allows us to solve for μk.