after a perfectly elastic collision of two identical balls one of which was initially at rest the velocity of both two are nonzero the angle theta between the final velocity
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That depends upon the condition of the two balls,
if they are perfectly rigid and there is no external force (including friction) is acting upon them, and no energy is converted into other forms such as heat and noise, they will rebound with the same speed and will land to the same place where they started (all kinetic energy will be converted to the same potential energy by which they started to move.). This is the case of Perfectly Elastic collision.
They will stop at the point of collision if all their kinetic kinetic energy is lost during collision (that may be the case of gluing where whole or some kinetic energy converts to potential energy of balls or case of deformation of balls). This is called Inelastic collision.
In all other cases they will not rebound with same speed. This is the actual case which occurs in practical scenario.
if they are perfectly rigid and there is no external force (including friction) is acting upon them, and no energy is converted into other forms such as heat and noise, they will rebound with the same speed and will land to the same place where they started (all kinetic energy will be converted to the same potential energy by which they started to move.). This is the case of Perfectly Elastic collision.
They will stop at the point of collision if all their kinetic kinetic energy is lost during collision (that may be the case of gluing where whole or some kinetic energy converts to potential energy of balls or case of deformation of balls). This is called Inelastic collision.
In all other cases they will not rebound with same speed. This is the actual case which occurs in practical scenario.
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