# Homework Help: Kinetic energy and work

1. Oct 25, 2008

### netrunnr

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 1.0m/s and then has the same kinetic energy as the son. what are the original speeds of the father and the son?
using k=1/2mv^2 and solving for v I did this:

M = mass K = kinetic energy V=velocity
d = (dad) father s = son i = initial f=final

Initial father
Md
Kdi
Vd

Initial son
Ms = 1/2 Md
Ks = 2Kdi
Vs

Kd = 1/2 Md (Vd )^2
Ks = 1/2 1/2 Md (Vd) ^2
2(1/2 Md (Vd)^2 = 1/2 1/2 Md Vs^2
2(2Vd^2 = 1/2 Vs^2
4Vd^2 = 1Vs^2

Final father
Md
Kdf
Vd+1.0ms
Final Son
Ms = 1/2 Md
Ks = Kdf
Vs

Kd = 1/2 Md (Vd +1)^2
Ks = 1/2 1/2 Md (V2)^2
1/2Md ( Vd +1)^2 = 1/2 1/2 Md Vs^2
now taking from initial the 4Vd^2 = 1Vs^2
(Vd +1)^2 = 1/2Vs^2
(Vd +1) ^2 = 1/2 4Vd^2
Vd^2 +2Vd + 1 = 2Vd^2
Vd^2 + 2Vd + 1 -2Vd^2 = 0
-Vd^2 +2Vd + 1 =0

I was trying to solve it at this point like a quadratic equation but I am lost because it seems unsolvable. I know I made a mistake and can't see where....

Last edited: Oct 25, 2008
2. Oct 25, 2008

### alphysicist

Hi netrunnr,

This is a typo; it should be Vs. (But it looks like you correct it in the next line.)

I don't believe this is correct, but it is probably just a typo because the next line is correct.

This line is correct, and so once you find the initial speed of the dad Vd, you can find the speed of the son.

It looks right to me. Just put it in the quadratic equation and solve. What do you get?