A running man has the same kinetic energy as that of a boy of half his mass. The man speeds up by `2 ms^(-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 

Options

A. 1/2
B. `2sqrt(2)`
C. `sqrt(2)`
D. `2`

Answer

B

Explanation

Let the mass of man be m.
Therefore, mass of the boy is `m/2`
As. `1/2 mv_1^2 = 1/2(m/2) v_2^2 :. v_1 = (v_2)/(sqrt2)`
`1/2 m(v_1 + 2)^2 = 1/2[m/2 (v_2 + x)^2]`
`:. (v_1 + 2)^2 = ((v_2 + x)^2)/(2) " or " v_1 + 2 = (v_2+ x)/(sqrt2)`
But `v_1 = (v_2)/(sqrt2) :. x/(sqrt2) = 2 " or " x = 2sqrt(2)`.