8.81. Set Up: For an elastic collision with object B initially at rest, and A is the alpha particle and B is the gold nucleus. Solve: Reflect: In an elastic collision of a light object with a stationary heavy object, the light object bounces back with its speed only slightly reduced. 8.82. Set Up: Take to be upward. Let A be the lower piece and B be the upper piece, so (a) Apply conservation of momentum to the explosion. (b) After the explosion the upper piece is in free-fall with At its maximum height Solve: (a) Explosion: gives so and (b) Motion after explosion: gives 8.83. Set Up: Apply conservation of momentum. Take to be to the right. For (a) the collision is elastic. Let A be the cart that is initially moving to the right. For (b) the two carts stick together and the combined object has final speed Solve: (a) gives and For an elastic collision This gives so and A rebounds with speed and B rebounds with speed (b) gives and Both carts are rest after the collision. Reflect:
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