00:02
For number 40, we have two balls having a head -on collision.
00:05
They are identical, so they have the same mass.
00:08
I called that m.
00:10
I called this ball one, and this will be ball two.
00:15
We know the velocities before the collision, and then we're to find their velocities after the collision.
00:21
I didn't even draw arrows, because i might not be sure which way they're going.
00:24
So i called this just v1, v2.
00:28
All right.
00:29
So it's an elastic collision.
00:31
So both momentum and kinetic energy are conserved.
00:35
So i set up my framework for this a way.
00:38
So the total momentum before the collision is equal to the total momentum after the collision.
00:43
They're all the same mass.
00:44
I'm going to cancel m out of these.
00:47
I'm dividing both sides by m before i even start.
00:51
So here i'm going to have 7 plus negative 4 equals v1 plus v2.
01:09
I can already tell where this is heading.
01:12
This is going to be a system of equations.
01:15
This equation has two variables in.
01:17
So that will that one.
01:18
So i'm going to go ahead and solve this a while for, i guess, v1.
01:25
So v1 will be 7 minus 4, 3 minus v2.
01:39
Okay.
01:40
And i'm going to work into conservation of energy.
01:43
Again, it's all the same mass.
01:45
I can cancel that.
01:46
I can divide everything by half.
01:54
So now i just have the velocities.
01:57
So here i'm going to have 7 squared and negative 4 squared will equal.
02:09
Oops, i didn't, so v1 squared plus v2 squared.
02:20
So i have 65 equals.
02:28
I'm going to do my substitution here.
02:30
So my v1 up here, i'm going to square it.
02:33
So i'm coming back up here to the top and v1 squared.
02:39
So i need to, you know, foil this out.
02:43
I need multiply binomials...