00:01
So here we have a quick schematic of a problem.
00:03
We have the first car denoted as one traveling at its velocity with its mass.
00:10
And we have the second car with an unknown mass sitting at rest.
00:15
And then after they collide, we have that they stick together and move at some velocity.
00:22
And to find this velocity, we are going to use conservation momentum, which says the initial momentum has to equal the final, where this is our initial situation and this is our final situation.
00:35
So if we look at the initial momentum, this will be the mass of the first object times the velocity of the first object here, plus the mass of the second object times the velocity of the second object, and the final velocity will therefore be the mass of the two objects together, which would be the sum of their masses, times their velocity, which was just vf.
01:02
And another thing we can add here is in the initial momentum up here the velocity of the second cart was zero so therefore this is just the momentum of the first cart and these two have to be equal so therefore m1 plus m2 times vf has to equal m1 times v1 and we want to solve for m2 here so we can divide by vf and subtract m1 from both sides to get that the second mass will be m1 v1 over vf minus m1...