A man who is running has half the kinetic energy of a boy of half his mass. The man speeds up by 1 `ms^(-1)` and then has the same kinetic energy as the boy. The original speed of the boy was:

Options

A. `sqrt2m//s`
B. `(sqrt2-1)m//s`
C. `(1)/((sqrt2-1))m//s`
D. `(1)/(sqrt2)m//s`

Answer

C

Explanation

Let m = mass of boy, M = mass of man
v = velocity of boy, V = velocity of man
`(1)/(2)MV^(2)=(1)/(2)[(1)/(2)mv^(2)] " "` …..(i)
`(1)/(2)M(V+1)^(2)=1[(1)/(2)mv^(2)] " "` …..(ii)
Putting `m = (M)/(2)` and solving `V= (1)/(sqrt(2)-1)`