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:
The kinetic energy equation is Ekinetic = ½ mv2. We can plug in the values given and set up a ratio to answer the question.
EX = ½ (100)(v)2
EY = ½ (10)(3v)2 = ½ (10)(9v2)
EX / EY = ½ (100)(v)2 / ½ (10)9v2
EX / EY = (100)(v)2 / (10)9v2
EX / EY = (10)(v)2 / 9v2
EX / EY = 10 / 9
Thus choice (A), 10:9 is the correct answer.