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A father racing his son has 1/3 the kinetic energy of the son, who has 1/3 the mass of the father. The father speeds up by 1.6 m/s and then has the same kinetic energy as the son.

So to being with, I set up two equations equal to each other, since the only unknown is initial velocity. I set it up as

(2/3)(1/2)(3m)(1.6)squared = (1/2)(3m)(v initial +1.6) squared

So to sum this up, I used 3m to represent the fathers weight in reference to the kid. The KE of the first half is multiplied times 2/3 because the increase of 1.6 m/s equalized the KE of the father and the boy, therefore the 1.6 m/s accounted for the other 2/3 of the energy. And on the other side, the v initial plus 1.6 m/s represented the final velocity that equaled the sons KE. I then cancelled out the 3m and the 1/2 and graphed the quadratic equation, but I am getting an answer of .359 m/s, and that is not right. How can i fix this, and am I even starting off correctly?

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# Kinetic Energy Question

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