When two billiard balls of equal mass ($m$) undergo a perfectly elastic head-on collision, what happens to their velocities ($v$) after the collision?

A $2\mathrm{kg}$ cart moving at $3m/s$ collides head-on with a $1\mathrm{kg}$ cart moving at $-2m/s$. After the collision, the $2\mathrm{kg}$ cart moves at $1m/s$ and the $1\mathrm{kg}$ cart moves at $4m/s$. What type of collision is this?

In a perfectly elastic collision between two perfectly rigid objects, which of the following quantities is conserved for the system as a whole?

A fake hockey puck of mass 4m has been rigged to explode. Initially the puck is at rest on a frictionless ice rink. Then it bursts into three pieces. One chunk, of mass m, slides across the ice at velocity vî. Another chunk, of mass 2m, slides across the ice at velocity 2v ĵ. Determine the velocity of the third chunk.

A neutron is an electrically neutral subatomic particle with a mass just slightly greater than that of a proton. A free neutron is radioactive and decays after a few minutes into other subatomic particles. In one experiment, a neutron at rest was observed to decay into a proton (mass 1.67×10^-27 kg) and an electron (mass 9.11×10^-31 kg) . The proton and electron were shot out back-to-back. The proton speed was measured to be 1.0 ×10⁵ m/s, and the electron speed was 3.0×10⁷ m/s. No other decay products were detected. How much momentum did this neutrino 'carry away' with it?

The nucleus of the polonium isotope ²¹⁴Po (mass 214 u) is radioactive and decays by emitting an alpha particle (a helium nucleus with mass 4 u). Laboratory experiments measure the speed of the alpha particle to be 1.92×10⁷ m/s . Assuming the polonium nucleus was initially at rest, what is the recoil speed of the nucleus that remains after the decay?

An object at rest on a flat, horizontal surface explodes into two fragments, one seven times as massive as the other. The heavier fragment slides 8.2 m before stopping. How far does the lighter fragment slide? Assume that both fragments have the same coefficient of kinetic friction.

A 195-kg projectile, fired with a speed of 116 m/s at a 60.0° angle, breaks into three pieces of equal mass at the highest point of its arc (where its velocity is horizontal). Two of the fragments move with the same speed right after the explosion as the entire projectile had just before the explosion; one of these moves vertically downward and the other horizontally. Determine the velocity of the third fragment immediately after the explosion.