So the basic problem in school we had was "two cars hitting eachother, calculate the speed after hit". We have been taught to use momentum (mv), but why not kinetic energy (0.5mvv)?
So for example, if one car weighting 10t and going 5m/s hits another 1t going 30 m/s, according to momentum would result in: 10000 * 5 - 1000 * 30 = 1.81 m/s going along with heavier car (because it had higher momentum).
Now if I calculate using kinetic energy: 10000 * 5 * 5 * 0.5 and 1000 * 30 * 30 * 0.5, I get 125kJ for heavier car and 450kJ for lighter. So it would result in 325kJ after hit and 7.68 m/s going along lighter car direction.
Why do we use momentum here?