00:01
In this problem, we want to take these two equations and prove that they implied that this equation must be true.
00:06
And we do that by eliminating t, because as you'll notice in this final equation, there is no t.
00:12
So to start out, i'm going to take this top equation and solve for t.
00:16
This is pretty straightforward.
00:18
I just subtract omega -0 and then divide by alpha.
00:21
So i get omega -mina -not over alpha.
00:25
And then now i'm going to take this value of t and plug it into the bottom equation.
00:29
So this gives theta minus theta not is equal to omega not times omega minus omega not over alpha, plus one half alpha, and then the whole thing squared.
00:45
So omega minus omega not over alpha squared.
00:52
Now what i'm going to do is i'm going to pull this alpha squared out of the parentheses and cancel it with one of these.
00:58
And then i'm going to multiply both sides of the equation by two alpha.
01:02
Whenever i do that, i get 2 alpha times theta minus theta not.
01:09
You'll see i multiply both sides by 2 alpha...