00:01
So in this question, we have an elastic collision of two bumper cars.
00:07
And we know their mass and respective velocity before the collision.
00:11
We want to know their velocity after the collision and the change of momentum of each.
00:17
So let's first try to figure out their velocities after the collision.
00:21
So two equations we have for elastic collision.
00:25
The first one is the relative velocity equation.
00:32
So this is the equation 7 .7.
00:35
So this formula says that the relative velocity of two objects will be equal and opposite before and after the collision.
00:44
And the second formula we need is the formula for the conservation of momentum.
00:52
So m -a -v -a plus mbv -b equals.
00:57
So momentum afterwards is m .ava prime plus mbvb prime.
01:07
So these two are the formulas we will need.
01:11
And we have two formulas and two unknowns, v .b.
01:15
So the first step is always to use the first formula to cancel one of the unknowns in the second formula.
01:24
So here i will express vb prime in terms of the rest of the quantities, vv .5.
01:30
Equals va minus vb plus va prime.
01:35
And then i will substitute this expression into the second one.
01:39
So i have m .a.
01:45
Plus m .b.
01:47
Vb.
01:48
Equals m .av.
01:51
Plus m .b.
01:55
Vas vb plus m .b.
01:59
Va.
02:00
Now i arrange everything to have m .a.
02:07
Prime on the left hand side and the rest on the right hand side.
02:11
So this gives us va prime equals mava plus mb so this is 2 times vb minus va and divided by f a plus mb now we plug e everything we have mava is is 435 kilograms times 4 .50 meters per second, plus mb is 495 kilogram times vb is 3 .7.
03:03
So 2 times 3 .7 meters per second.
03:07
Subtract 4 .5 meters per second.
03:13
So it's 7 .2 minus 4 .5 .5 .5 .5.
03:16
Of simple 4 and 4 .5 which is like 2 .9...