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The book solves this question by getting the final speed in terms of elastic collision.

I understand all the example but what I don't understand is we here used elastic collision but isn't elastic collision defined when there is no loss of kinetic energy ? so why then we would use elastic collision in this case ? I know its stated in the problem,but what I don't understand is that kinetic energy is defined for elastic collision to be when there is no loss in kinetic energy thats what I don't understand about this problem.