A \(0.50\,\mathrm{kg}\) cart moving at \(8.0\,\mathrm{m\,s^{-1}}\) sticks to a \(1.5\,\mathrm{kg}\) cart at rest. Find the final speed.

A \(2.0\,\mathrm{kg}\) cart changes velocity from \(5.0\,\mathrm{m\,s^{-1}}\) right to \(1.0\,\mathrm{m\,s^{-1}}\) left. Find the impulse on it, taking right as positive.

A collision conserves total momentum but the objects stick together. Is the collision elastic?

A \(3.0\,\mathrm{kg}\) cart moving at \(4.0\,\mathrm{m\,s^{-1}}\) sticks to a \(2.0\,\mathrm{kg}\) cart moving in the same direction at \(1.0\,\mathrm{m\,s^{-1}}\). Find their final speed.

A \(1.0\,\mathrm{kg}\) cart moving at \(6.0\,\mathrm{m\,s^{-1}}\) sticks to a \(2.0\,\mathrm{kg}\) cart at rest. Find the kinetic energy lost.

A \(2.0\,\mathrm{kg}\) cart moving east at \(3.0\,\mathrm{m\,s^{-1}}\) sticks to a \(2.0\,\mathrm{kg}\) cart moving north at \(4.0\,\mathrm{m\,s^{-1}}\). Find the final velocity vector.

A \(0.20\,\mathrm{kg}\) ball moving east at \(15\,\mathrm{m\,s^{-1}}\) hits a wall and leaves west at \(10\,\mathrm{m\,s^{-1}}\). Find the impulse from the wall and state what happens to the wall's momentum.

A \(1000\,\mathrm{kg}\) car moving east at \(20\,\mathrm{m\,s^{-1}}\) collides and locks with a \(1500\,\mathrm{kg}\) van moving north at \(12\,\mathrm{m\,s^{-1}}\). Find the wreckage speed and direction.

A \(0.020\,\mathrm{kg}\) projectile embeds in a \(1.98\,\mathrm{kg}\) block suspended as a pendulum. After the collision, the block-projectile system rises \(0.20\,\mathrm{m}\). Find the projectile's speed before impact. State which conservation law applies during each stage and why.

A projectile of mass \(m\) embeds in a block of mass \(M\) attached to a horizontal spring of stiffness \(k\). The surface is frictionless and the spring compresses by maximum distance \(x\). Derive the projectile's incoming speed. Explain why mechanical energy is not conserved during the collision.