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

`1/2Mv^2=1/2[1/2mv^2]" "...(i)`
`1/2 M(v+1)^2 =1/2 mv^2 " "...(ii)`
[Here `m=M/2` ]
By (i) and (ii) -
`v^2/((v+1)^2)=1/2implies v/(v+1)=1/sqrt2`
`implies sqrt2v=v+1`
`implies sqrt2v=v+1`
`implies v(sqrt2-1)=1`
`implies v = 1/(sqrt2-1) m//s`