Posted by **Bill** on Saturday, March 5, 2011 at 11:37pm.

A father racing his son has one-third the kinetic energy of the son, who has two-fifths the mass of the father. The father speeds up by 1.5 m/s and then has the same kinetic energy as the son.

What is the Father's initial speed?

What is the Son's initial speed?

- Physics Concepts -
**drwls**, Sunday, March 6, 2011 at 1:41am
Let the father's mass be M sos that the son's mass must be 2M/5. Let the father's initial speed be V, and the son's v.

(1/2)MV^2 = (1/3)(2M/5)v^2

which leads to

V^2 = (4/15)v^2

(1/2)M(V +1.5)^2 = (2M/5) v^2

V^2 + 3V + 2.25 = (4/5) v^2

3V^2 = (4/5)v^2

Now you can eliminate v.

2V^2 -3V -2.25 = 0

That can be solved for a positive V using the quadratic equation. Chack my math.

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