You are in a sledding contest where you start at a height of 40.0 m above the bottom of a valley and slide down a hill that makes an angle of 25.0° with respect to the horizontal. When you reach the valley, you immediately climb a second hill that makes an angle of 15.0° with respect to the horizontal. The winner of the contest will be the contestant who travels the greatest distance up the second hill. You must now choose between using your fl at-bottomed plastic sled, or your “Blade Runner,” which glides on two steel rails. The hill you will ride down is covered with loose snow. However, the hill you will climb on the other side is a popular sledding hill, and is packed hard and is slick. The two sleds perform very differently on the two surfaces, the plastic one performing better on loose snow, and the Blade Runner doing better on hard-packed snow or ice. The performances of each sled can be quantified in terms of their respective coefficients of kinetic friction on the two surfaces. For the plastic sled: ???? = 0.17 on loose snow, and ???? = 0.15 on packed snow or ice. For the Blade Runner, ???? = 0.19 on loose snow, and ???? = 0.07 on packed snow or ice. Assuming the two hills are shaped like inclined planes, and neglecting air resistance,

(a) How far does each sled make it up the second hill before stopping?

(b) Assuming the total mass of the sled plus rider is 55.0 kg in both cases, how much work is done by nonconservative forces (over the total trip) in each case?