Question

A running man has half the KE that a body of half his mass has. The man speeds up by `1.0ms^(-1)` and then has the same energy as the boy. What were the original speeds of the man and the boy?
A. `(sqrt2+1),(sqrt2-1)`
B. `(sqrt2+1),2(sqrt2+1)`
C. `sqrt2,sqrt2`
D. `(sqrt2+1),2(sqrt2-1)`

Answer 1

Correct Answer - B
(b) According to the question, `(1)/(2) mv_(1)^(2)=(1)/(2)[(1)/(2)xx(m)/(2)xxv_(2)^(2)]`
where, `v_(1)="speed of man and "v_(2)`=speed of boy
Now, `(1)/(2)m(v_(1)+1)^(2)=(1)/(2)xx(m)/(2)xxv_(2)^(2)`
Solving these two equations we get, `v_(1)=(sqrt2+1)ms^(-1)` and `v_(2)=2(sqrt2+1)ms^(-1)`