00:01
Okay, so we have the magnitude and direction exerted by two tuckboats towing a ship are 1610 kilograms north, 35 degrees west.
00:14
So let's just put this on a coordinate system first, where this is quadrant 1, quadrant 2, quadrant 3, and quadrant 4.
00:24
So it's saying north, 35 degrees west.
00:28
So we're here.
00:33
This angle is 35 degrees, and the magnitude of the vector is 1610.
00:42
And then 1250 kilograms south, 55 degrees west.
00:49
So it's here where this angle is 55 degrees, and the magnitude is 1250.
01:00
So we want to find the magnitude and direction of the resultant force.
01:06
Okay, so the way i like to do these problems is first we can get rid of these first two quadrants, or quadrant one and quadrant four, just so we have room to write on the other side of it.
01:21
Okay, so first let's look at this triangle.
01:29
So we have the top triangle where this angle is third.
01:37
35 degrees and the hypotenuse has a distance of 1610.
01:43
So that's the magnitude of the vector.
01:45
So let's find the x and y components.
01:52
So to find the x component, so sign is opposite over hypotenuse.
02:02
So this is the opposite, this is the adjacent.
02:08
So we have sign of, of 35 is equal to the opposite over 1610.
02:30
And we have the cosine of 35 degrees is equal to the adjacent over 1610.
02:47
Okay, solving these two.
02:49
First, we see that the opposite is equal to 1610 times the sign of 35 degrees.
03:03
So make sure your calculator is in degree mode and we find that the sign of 35 degrees, let me just open my calculator, sorry, there we go.
03:27
So the sign of 35 degrees is 0 .57.
03:32
If we multiply this by 1610, gives us 923 .46.
03:42
Okay, so now we need to find the adjacent of the top triangle.
03:59
So the adjacent is 1610 times cosine of 35 degrees.
04:05
So cosine of 35 degrees is .82.
04:11
Multiply that by 1610.
04:14
And this is 13, 18 .83.
04:25
Okay, so now let's look at the bottom triangle and then we'll put it all together.
04:29
So the bottom triangle, it looks like this, it's a right triangle here.
04:41
So this is 55 degrees and the hypotenuse is 1250...