Two model trains are propelled along a straight, frictionless track by electric motors. Train X has a total mass of 100g and is moving at speed v. Train Y has a total mass of 10g and is moving at speed 3v. The ratio of the kinetic energies of Train X to Train Y is:

A) 10:9

B) 9:10

C) 10:3

D) 1:9

**Explanation**

The kinetic energy equation is Ekinetic = ½ mv2. We can plug in the values given and set up a ratio to answer the question.

E_{X} = ½ (100)(v)^{2}

E_{Y} = ½ (10)(3v)^{2} = ½ (10)(9v^{2})

E_{X} / E_{Y} = ½ (100)(v)^{2} / ½ (10)9v^{2}

E_{X} / E_{Y} = (100)(v)^{2} / (10)9v^{2}

E^{X} / E^{Y} = (10)(v)^{2} / 9v^{2}

E_{X} / E_{Y} = 10 / 9

Thus choice (A), 10:9 is the correct answer.