Conservation of Momentum — Prelims Questions

A $2\,\text{kg}$ mass moving at $10\,\text{m/s}$ collides head-on with a $4\,\text{kg}$ mass moving at $5\,\text{m/s}$ in the opposite direction. If the collision is perfectly inelastic, what is the final velocity of the combined mass?

A bullet of mass $20\,\text{g}$ is fired from a gun of mass $5\,\text{kg}$. If the bullet leaves the gun with a velocity of $400\,\text{m/s}$, what is the recoil velocity of the gun?

Which of the following statements is TRUE regarding an elastic collision?

A $10\,\text{kg}$ object moving at $4\,\text{m/s}$ explodes into two pieces. One piece of mass $4\,\text{kg}$ moves at $8\,\text{m/s}$ in the original direction. What is the velocity of the second piece?

A ball of mass $m$ moving with velocity $v$ collides with another ball of mass $M$ at rest. If the collision is perfectly elastic, and $m \ll M$, what is the approximate final velocity of the ball of mass $m$?

A $0.5\,\text{kg}$ ball is dropped from a height of $1.8\,\text{m}$ onto a hard floor. It rebounds to a height of $0.8\,\text{m}$. What is the magnitude of the impulse imparted by the floor to the ball? (Take $g = 10\,\text{m/s}^2$)