A man running has half the kinetic energy of a boy half his mass. The man speeds up by 1 `ms^(-1)` and then has kinetic energy sa that of the boy. What wre the original speed of man and the boy ?

Options

A. `sqrt(2) ms^(-1), 2sqrt(2) -1 ms^(-1)`
B. `(sqrt(2) -1) ms^(-1), 2(sqrt(2) -1) MS^(-1)`
C. `(sqrt(2) + 1) ms^(-1) , 2 (sqrt(2) + 1) ms^(-1)`
D. None of these

Answer

C

Explanation

Let mass of boy be m, therefore, mass of man = 2 m,
As, KE of man ` = (1)/(2)KE` of boy `therefore (1)/(2) (2m)u^(2) = (1)/(2) xx (1)/(2) mu^(2)`
`u^(2) = (u.^(2))/(4), u = (u.)/(2)`
When man speeds upto 1 m/s.
KE of man = KE of boy `(1)/(2) (2m) (u +1)^(2) =(1)/(2)mu^(.2) = (1)/(2)m(2u)^(2), (u + 1)^(2) = 2u^(2)`
`u + 1 = sqrt(2)u, u = (1)/(sqrt(2-1)) = (sqrt(2) +1)/((sqrt(2)-1)(sqrt(2)+1)), u = (sqrt(2)+1)ms^(-1)`
`u. = 2u = 2(sqrt(2) +1)ms^(-1)`