A running man has half the kinetic energy of that of a boy of half of his mass. The man speed up 1 ~m / s , so as the have same kinetic energy as that of a boy. The original speed of the man is

Step-by-step solution

The kinetic energy of moving body is equal to half the product of the mass (m) of the body and the square of its speed (v^2 ) . kinetic energy = 1 2 mass ( speed )^2 i.e., = 1 2 m v^2 Let mass of man is M ~kg and speed is v and speed of body is v₁ , then 1 2 M v^2= 1 2 1 2 M 2 v₁^2 .....(i) when man speed up by 1 ~m / s , than v=v+1 1 2 M(v+1)^2= 1 2 M 2 v₁^2 ....(ii) Dividing Eqs. (i) by (ii), we get v^2 (v+1)^2 = 1 2 2 v=v+1v= 1 2 -1 ~m / s