A $1500 \text{ kg}$ car is traveling at $20 \text{ m/s}$. The driver applies the brakes, resulting in a constant braking force of $6000 \text{ N}$. How long will it take for the car to stop?

A $10,000 \text{ kg}$ train car A traveling at $5 \text{ m/s}$ strikes a stationary $15,000 \text{ kg}$ train car B. The cars couple together (perfectly plastic impact). Determine their common velocity after the collision and the percentage of kinetic energy lost.

Two identical hockey pucks, A and B (mass $m = 0.15 \text{ kg}$ each), slide on a frictionless horizontal ice surface. Puck A is moving at $4 \text{ m/s}$ along the x-axis and strikes puck B, which is initially at rest. The collision is perfectly elastic ($e = 1$). After the collision, puck A moves off at an angle of $30^\circ$ above the x-axis. Determine the final velocities of both pucks and the direction of puck B's motion.

A tennis ball and a seemingly identical "sad" ball (made of a highly inelastic rubber compound) are dropped simultaneously from the same height onto a hard floor. The tennis ball rebounds to a significant portion of its original height, while the sad ball barely bounces at all. Analyze the physical differences in these collisions in terms of impulse, deformation, and the coefficient of restitution ($e$).

A stationary cannon fires a heavy projectile horizontally. The cannon immediately recoils backward. Analyze this event using the principle of conservation of momentum. Explain why the cannon recoils much slower than the projectile travels forward, and how a recoil mechanism (like a spring-damper system) utilizes impulse to safely stop the cannon.