00:01
So here we basically have some geometry to work out with our vector.
00:06
So we have our coordinates, our vector, somewhere up here.
00:13
These are always fun to draw, all these at an angle so it's not that bad.
00:20
So we have our force f, which we ultimately want to find our components for.
00:25
And so we want to find the x, y, z components of that.
00:27
So we want to find the components that are perpendicular and parallel to the axis.
00:37
Now we conveniently already have one here.
00:40
The h is upwards, so that is just directly our z component, basically.
00:45
So that's our z component, our y component, and our x component.
00:50
Now we're given the lengths of these, 3 .1 kilonewton, 4 .5 kilonewton, and 7 .7 kilonewton.
01:02
So we have our first component already, but we need to do some geometry on the xy plane here and this angle 21 degrees.
01:11
So notice that we have a triangle here, and so that's going to be helpful.
01:15
We have two sides and an angle, so that is enough to define the triangle completely.
01:21
We're going to look at the law of sines, which says the sine of the angle, and so i'm going to look at this angle alpha here that we want to solve for.
01:32
Now we can tell this is going to be helpful.
01:33
We know the length here, we have this angle, we can then work out the components very quickly.
01:37
So the sine of our angle alpha over the opposite side, so the 4 .5.
01:43
So this relationship, the sine of the angle and the opposite side lengths are equal across the triangle.
01:53
So the sine of the 21 degree angle here is over 7 .7 is also equal, so we see that pair here...