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netrunnr
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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...
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: