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To calculate the final velocities of two objects after a two dimensional elastic collision with unequal masses, you can use the equations:
V1f = (m1 - m2)/(m1 + m2) * V1i + (2 * m2)/(m1 + m2) * V2i
V2f = (2 * m1)/(m1 + m2) * V1i + (m2 - m1)/(m1 + m2) * V2i
where m1 and m2 are the masses of the two objects, V1i and V2i are the initial velocities of the objects, and V1f and V2f are the final velocities of the objects.
An elastic collision is a type of collision in which both kinetic energy and momentum are conserved. This means that the total kinetic energy before the collision is equal to the total kinetic energy after the collision, and the total momentum before the collision is equal to the total momentum after the collision. In contrast, an inelastic collision is a type of collision in which kinetic energy is not conserved. Some of the kinetic energy is lost during the collision, usually in the form of heat or sound.
The angle of deflection in a two dimensional elastic collision is calculated using the equation:
θ = tan^-1((V1i * sin α1 + V2i * sin α2)/(V1i * cos α1 - V2i * cos α2))
where V1i and V2i are the initial velocities of the two objects, and α1 and α2 are the angles at which the objects are initially moving.
No, the kinetic energy of an object cannot decrease after a two dimensional elastic collision. In an elastic collision, the total kinetic energy is conserved, meaning that it remains the same before and after the collision. However, the kinetic energy of each individual object may change as a result of the collision.
Some real-life examples of two dimensional elastic collisions with unequal masses include billiard balls colliding on a pool table, two cars colliding at an intersection, or a tennis ball hitting a tennis racket. In all of these scenarios, the objects have different masses and collide with each other, resulting in a change in their velocities and directions.