Afather racing his son has 1/3 the kinetic energy of the son, who has 1/4 the mass of the father. the father speeds up by 1.5 m/s and then has the same kinetic energy as the son. what are the original speeds of
(a) the father and
(b) the son?

Explanation:

Let the speeds of father and son are . The kinetic energies of father and son are . The mass of father and son are  

(a) According to given conditions,

And

Kinetic energy of father is given by :

.............(1)

Kinetic energy of son is given by :

...........(2)

From equation (1), (2) we get :

..............(3)

If the speed of father is speed up by 1.5 m/s, so the ratio of kinetic energies is given by :

Using equation (3) in above equation, we get :

(b) Put the value of in equation (3) as :

Hence, this is the required solution.