Question

A father racing his son has half the kinetic energy of the son,
who has half the mass of the father. The father speeds up by 1.0 m/s
and then has the same kinetic energy as the son. What are the orige
nal speeds of (a) the father and (b) the son?
need with step by step .​

Answer 1

We denote the mass of the father as m and his initial speed vi. 

The initial kinetic energy of the father is

Ki=21Kson

and his final kinetic energy (when his speed is vf=vi+1.0m/s) is 

Kf=Kson.

(a) We see from the above that Ki=21Kf, which (with SI units understood) leads to

21mvi2=21[21m(vi+1.0m/s)2].

The mass cancels and we find a second-degree equation for vi.

21vi2−vi−21=0.

The positive root (from the quadratic formula) yields vi=2.4m/s

(b) From the first relation above 

(Ki=21K