A running man has the same kinetic energy as that of a boy of half his mass. The man speed up by 2 m s - 1 and the boy changes his speed by x m s - 1 , so that the kinetic energies of the boy and the man are again equal. Then x in m s - 1 is

Question

A running man has the same kinetic energy as that of a boy of half his mass. The man speed up by 2 m s - 1 and the boy changes his speed by x m s - 1 , so that the kinetic energies of the boy and the man are again equal. Then x in m s - 1 is, 4 2, 2 2, 2, 2

MARKS App · Accepted Answer

Let v M be velocity of man, v B of boy, then kinetic energy according to question , i e K = 1 2 M v M 2 = 1 2 . M 2 . v B 2 Or v M 2 = V B 2 2 Or 2 v M = v B When the man speeds up 2 m s - 1 and the boy changes his speed by x m s - 1 .Then , 1 2 M v M + 2 2 = 1 2 ⋅ M 2 ⋅ v B + x 2 Or v M + 2 2 = v B + x 2 2 2 v M + 2 2 = 2 v M + x 2 ∵ v B = 2 v m Or 2 v M + 2 = 2 v M + x Or x = 2 2

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