You and your friend are sledding on two sides of a triangle-shaped hill. On your side, the hill slopes up at 30.0° from the horizontal; on your friend's side, it slopes down at the same angle. You do not want to climb up the hill, so you tell your friend to thread a rope through an ideal pulley that is conveniently atop the hill. He connects the rope to his sled and tosses the other end of the rope to you. The sleds on the snow have a coefficient of kinetic friction, μk, of 0.0500. The total mass of your friend and his sled is 82.0 kg while you and your sled have a mass of 68.0 kg. (a) What is the magnitude of the acceleration of each sled? (b) What is the tension in the rope?
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