The K.E. of a person is just half of K.E. of a boy whose mass is just half of that person. If person increases its speed by 1 m/s, then its K.E. equals to that of boy then initial speed of person was -

Options

A. `(sqrt(2)+1)`m/s
B. `(2+sqrt(2))` m/s
C. `2(sqrt(2)+2)` m/s
D. None

Answer

A

Explanation

Let initial speed of man of mass m be u then
`KE_(man)=1/2"mu"^2" & "KE_(boy)=2xx1/2"mu"^2="mu"^2`
Now if man increases his speed by `1 m//s^(-1)` then
`KE_(man)=1/2m(u+1)^2=KE'_(boy)="mu"^2`
`(u+1)/(u)=sqrt2`
`u=1/(sqrt2-1)xx(sqrt2+1)/(sqrt2+1)=(sqrt2+1)ms^-1`