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 speeds of the man and the boy was:

Options

A. `2 m//s`
B. `9.6 m//s`
C. `4.8 m//s`
D. `7.2 m//s`

Answer

C

Explanation

If original speed of boy is then
`1/2 M v^2 = 1/2[1/2 M/2 v_0^2] " "….(i)`
Also, `1/2 M (v + 1)^2 = 1/2 M/2 v_0^2 " "…..(ii)`
From Eqs. (i) and (ii) `" "((v + 1)/v)^2 = 2 implies v = 1/(sqrt(2) - 1) , " " v = sqrt(2) + 1 = 2.41 m//s`
From equation (i), `v_(0) = 2 v = 4.8 m//s` .