You and your friend find yourselves in an unfortunate situation. A shopping-cart-related stunt has gone wrong and now your friend is stuck in a shopping cart and is on a crash course for your house with speed V= 2.65~\mathrm{m/s}V=2.65 m/s. You are on the roof of your house, which forms an angle \theta = 40.0^{\circ}θ=40.0 ∘ with the horizontal, and it's your job to stop your friend. You size up the situation and see that the mass of your friend and the cart combined is M = 40.1~\mathrm{kg}M=40.1 kg and luckily you have some camera equipment with you whose total mass is m = 35.4~\mathrm{kg}.m=35.4 kg. Your plan is as follows. You're going to climb up the roof, place the equipment on the (frictionless) rooftoop, and let it slide off the roof, which is a height h=4.21~\mathrm{m}h=4.21 m above the ground. Your friend is going to catch the equipment and get slowed down by it. How far up the roof do you need to climb in order for your friend to come a complete stop?
