A running man has half the kinetic energy of that of a boy of half his mass. The man speeds up by one metre per second and then has the same kinetic energy as that of the boy. What are the original speeds of the boy and man?

Options

A. `(4.8:2.4)ms^(-1)`
B. `(3.6:1.8)ms^(-1)`
C. `(2.4:1.2)ms^(-1)`
D. `(9.8:4.9)ms^(-1)`

Answer

a

Explanation

Here, let `v_m` and `v_b` the speeds of man and boy respectively.
Then `1/2mv_(m)^(2)=1/2[1/2xxm/2xxv_b^2]` or `v_b^2=4v_m^2`
or `v_b=2v_m`
Also `1/2m(v_m+1)=1/2xxm/2ccv_b^2`
`:. 2v_m^2-4 v_m-2=0`
Solving the quadratic
`v_m=1+sqrt2=1+1.4=2.4 ms^(-1)`
`:. v_b=2xx2.4=4.8 ms^(-1)`.