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?(adsbygoogle = window.adsbygoogle || []).push({});

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....

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# Homework Help: Kinetic energy and work

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