Asled is being held at rest on a slope that makes an angle θ with the horizontal. after the sled is released, it slides a distance d1 down the slope and then covers the distance d2 along the horizontal terrain before stopping. find the coefficient of kinetic friction μk between the sled and the ground, assuming that it is constant throughout the trip.

mu_k =d_{1}\frac{{\sin}\left({\theta}\ri ght)}{\left(d_{2}+d_{1}{\cos}\left( {\theta}\right)\right)} (this is correct! )
suppose the same sled is released from the same height on the same slope. this time, however, assume that the coefficient of kinetic friction between the ground and the sled is a known quantity, mu, and, as before, constant throughout the trip. after the sled is released, it slides the same distance d_1 down the slope and then moves a certain (unknown) distance along the horizontal terrain before stopping. find the distance d traveled by the sled from the end of the slope until it comes to a stop.

express your answer in terms of the variables d_1, mu, and theta.