Posted by **Chris** on Thursday, December 14, 2006 at 4:22pm.

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 m/s and then has the same kinetic energy as the son. What are the original speeds a) of the father? b) of the son?

I know that KE=1 for the son and he has 1/2mass. The father has 1/2 KE and 1 mass. Should I use v^2=V_i^2 +2ad?

How would I do this?

Let V be the initial velocity of the son, and M be his mass The father's initial speed must be V/2, so that

(KE)son = (1/2) M V^2

(KE)father = (1/2)*(2M)*(V/2)^2

= (1/2)(KE)son

You also know that

(1/2)(2M)[(V/2) +1]^2= (1/2) M V^2

2M [(V/2) +1]^2 = MV^2

2[(V/2) +1]^2 = V^2

This will lead to a quadratic equation for V. Solve for V, and then V/2, the father's initial speed.

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