a father his son has half the kinetic energy of the son, who hashalf the mass of

Question

a father his son has half the kinetic energy of the son, who hashalf the mass of the father. The father speeds up by anamount v and then has the same kinetic energy as theson. Show that the fathers original speed is given by
        vf= v(1 + 2)

i tried finding the kinetic energy of each and then setting themequal to each other and that did not work. I think the rightway to go about this is to use the work kinetic energy theorem, butim not sure how to set that up with this. Any help would beawesome

Explanation / Answer

Let's try it your way again: Data: mass of father=M ; mass of son=M/2 KE father= K/2 ; KE son =K for father: K/2=1/2*M*vf2                  i.e:K=M*vf2 --(1) for son: K=1/2*M/2*vs2 --(2) equating (2) to (1): 1/2*M/2*vs2=M*vf2 vf2=1/4vs2 vf=1/2vs  --(3)Now we know that the original speed of thefather is half the original speed of the son. Now new vf= vf+v so new KE=1/2*M*(vf+v)2=1/2*M/2*vs2 --(equating to son's KE) substituting value of vs from (3): 1/2*M*(vf+v)2=1/2*M/2*4vf2 (vf+v)2 =2vf2square rooting both sides: vf+v =vf2 v=vf(2-1) vf=v/(2-1) Now all you have to do is rationalize the denominator bymultiplying and dividing the RHS by (1+2) and you get: vf = v(1 +2) Tah-dah !

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