Vehicles are designed to crumple during a collision as a safety mechanism. Crumpling increases the duration of the impact, which reduces the force experienced by the passengers due to the impulse-momentum relationship. While momentum is conserved in the collision, kinetic energy is partially converted into other forms of energy, including the energy absorbed in deforming the vehicle. This deformation helps in dissipating the energy of the collision over a longer time and a larger area, reducing the severity of the impact on the occupants. Thus, the crumple zones in vehicles are a direct application of momentum conservation principles for safety.

Yes, momentum can be conserved in a system where kinetic energy is lost. This scenario typically occurs in inelastic collisions, where the colliding objects might stick together or deform, resulting in a loss of kinetic energy, usually converted into other forms like heat or sound. Despite this energy transformation, the total momentum of the system before and after the collision remains constant. This is because momentum conservation depends on the mass and velocity of the objects, not on the kinetic energy. Therefore, even when kinetic energy is not conserved, the principle of momentum conservation still applies.

In two-dimensional elastic collisions, the angle at which the objects collide significantly influences the outcome. When two objects collide at an angle, their momentum and kinetic energy are distributed among the two dimensions. The conservation of momentum is applied separately along the x and y axes. The angle of collision changes the direction of the velocity vectors post-collision, affecting their final trajectories and speeds. For example, in a pool game, the angle at which the cue ball strikes another ball determines the directions in which they move after the collision. Analysing these collisions requires resolving the velocities into their components along each axis.

Understanding collisions in sports is vital for both enhancing performance and ensuring safety. For athletes, knowledge of how momentum is conserved during impacts helps in executing movements that maximise efficiency and effectiveness. For example, tennis players use the principles of collision to optimise their racket swings to transfer maximum momentum to the ball. In terms of safety, understanding collision dynamics is crucial in designing protective gear like helmets and pads that effectively absorb and redistribute impact forces, reducing the risk of injury. This understanding is also applied in creating safer sports equipment and playing surfaces.

In space exploration and satellite deployment, momentum conservation is a fundamental principle guiding spacecraft manoeuvres. In the vacuum of space, where external forces like air resistance are negligible, the conservation of momentum is crucial for accurately controlling spacecraft movement. Techniques such as using thrusters to expel gases in one direction, thereby propelling the spacecraft in the opposite direction, are based on momentum conservation. Additionally, when deploying satellites, the momentum transferred to the satellite must be carefully calculated to ensure it reaches the desired orbit. These manoeuvres rely on precise calculations based on momentum conservation to achieve the necessary speed and direction.