1. Impulse and velocity analysis, calculating the speed of a particle after receiving an impulse and finding the angle between its initial and final direction of motion. 2. Equilibrium of a uniform lamina under applied force, determining the required force in terms of the weight of the lamina. 3. Work-energy principle, calculating the power required for constant speed and the distance a trailer travels after detaching from the car. 4. Particle motion analysis, determining the force acting on a particle based on its velocity function and calculating its position vector at a specific time. 5. Collision dynamics, finding the speed of particles after a collision and determining the coefficient of restitution in a system with multiple interactions. 6. Mechanics involving equilibrium and forces on a rod resting on a hemisphere, calculating the normal reaction and forces at equilibrium, and finding the angle of the rod.