Advanced Problems

1. Three particles with masses 1 kg, 2 kg, and 3 kg move along a straight line with velocities 2, -1, and 3 m/s. Find the center of mass velocity and total momentum.
2. Two carts, 2 kg and 3 kg, collide inelastically at velocities 5 m/s and 2 m/s. After the collision, they hit a wall elastically. Compute final velocities.
3. A 5 kg ball moving at 8 m/s collides elastically with a stationary 5 kg ball. Determine post-collision velocities and kinetic energy change.
4. Four particles in a 2D plane collide elastically. Masses: 1 kg, 2 kg, 3 kg, 4 kg. Initial velocities given. Find final velocities using momentum conservation in x and y directions.
5. Two cars of masses 1200 kg and 1000 kg collide inelastically at 15 m/s and 5 m/s. Determine final velocity and loss in kinetic energy.