A \(1.0\,\mathrm{kg}\) cart moving at \(4.0\,\mathrm{m\,s^{-1}}\) elastically hits an identical cart at rest in one dimension. Find both final velocities.

In a one-dimensional elastic collision, what happens to the relative speed of separation compared with the relative speed of approach?

A \(1.0\,\mathrm{kg}\) cart moving at \(8.0\,\mathrm{m\,s^{-1}}\) elastically hits a \(3.0\,\mathrm{kg}\) cart at rest. Find the final velocities.

A \(2.0\,\mathrm{kg}\) cart moving at \(5.0\,\mathrm{m\,s^{-1}}\) elastically hits a \(1.0\,\mathrm{kg}\) cart at rest. Find both final velocities.

Two identical carts collide elastically in one dimension. Cart A has initial velocity \(3.0\,\mathrm{m\,s^{-1}}\); cart B has initial velocity \(-1.0\,\mathrm{m\,s^{-1}}\). Find the final velocities.

A small ball elastically rebounds from a massive stationary wall. If it approaches at \(7.0\,\mathrm{m\,s^{-1}}\), find its final velocity in the wall frame.

A \(0.20\,\mathrm{kg}\) ball moving at \(6.0\,\mathrm{m\,s^{-1}}\) elastically hits a stationary target. The ball rebounds at \(2.0\,\mathrm{m\,s^{-1}}\). Find the target mass and target final speed.

Show that identical masses exchange velocities in a one-dimensional elastic collision. State which two equations are being combined.

A \(2.0\,\mathrm{kg}\) cart moving right at \(5.0\,\mathrm{m\,s^{-1}}\) collides elastically with a \(3.0\,\mathrm{kg}\) cart moving left at \(1.0\,\mathrm{m\,s^{-1}}\). Find both final velocities, then verify momentum and kinetic energy.

For a one-dimensional collision with coefficient of restitution \(e\), derive \(v_1\) for mass \(m_1\) striking a stationary mass \(m_2\). Then state the condition for \(m_1\) to rebound. Interpret the elastic case.