An elastic collision is a type of collision between two objects where there is no loss of kinetic energy. This means that the total kinetic energy before and after the collision is the same.
In an elastic collision, the total momentum of the system before and after the collision is conserved. This means that the sum of the momenta of the two objects before the collision is equal to the sum of the momenta after the collision.
The equation for calculating the final velocities in an elastic collision is:
v1 = (m1 - m2)v1i + 2m2v2i / (m1 + m2)
v2 = 2m1v1i - (m1 - m2)v2i / (m1 + m2)
where m is the mass of the object and vi is the initial velocity before the collision.
In an elastic collision, the total kinetic energy is conserved, while in an inelastic collision, some kinetic energy is lost. In an inelastic collision, the objects may stick together or deform, while in an elastic collision, they bounce off each other without any deformation.
To solve for the velocities in an elastic collision algebraically, you can use the equations v1 = (m1 - m2)v1i + 2m2v2i / (m1 + m2) and v2 = 2m1v1i - (m1 - m2)v2i / (m1 + m2). Plug in the known values for the masses and initial velocities, and solve for the final velocities.