Question

A father racing his son has 1/ 4 the kinetic energy of the son, who has 1/ 3 the mass of the father. The father speeds up by 1.4 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?

Answer 1

Kinetic energy of an object having mass ' m ' and speed v is given by

  

Let the initial kinetic energy, mass and the initial speed of the father is , M , and respectively. And let the initial kinetic energy , mass, and the initial speed of the son is , ,and respectively.

So, initial kinetic energy of the father is

  

and initial kinetic energy of the son is

Given,

and   

i.e.   

or,   

or,   

or, .......................................(1)

It is also given that when the father speeds up by 1.4 m/s and then has the same kinetic energy as the son. i.e.

or,   

or,

or,

Using equation (1), we get

  

or,

or,   

or,

or,

Here, we will not consider the negative value of the speed as speed can't be negative.

Putting these values in equation (1), we get  

or,  

Hence,

(a) Original speed of the father is 1.4 m/s .

(b) Original speed of the son is 4.8497 m/s .

For any doubt please comment and please give an up vote. Thank you.