Q4. The momentum of the miser and his gold is initially zero since both are at rest. No horizontal external forces act on the miser-gold system and its momentum must therefore be conserved in the horizontal direction.. If the miser throws some gold in one direction, he will recoil in the opposite direction such that the sum of his momentum and the gold's momentum is zero. Although the center of mass of the miser-gold system doesn't move, the miser moves in one direction as the gold moves in the other. The miser can therefore get off of the ice at the cost of some of his gold.
Q7. An external impulse (= force acting x time over which the force acts) is required to change your momentun to zero in an auto crash. By having the car crumble, the crash takes more time and therefore a smaller force is required to bring you to rest. If the car doesn't crumble you will come to rest in less time which means a larger force must act on you. Since the forces acting on you do all the damage, the smaller the net force acting on you the better.
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