00:01
All right, so we got this boat traveling.
00:02
Let's draw a little picture.
00:04
The boat is traveling.
00:06
So here's our little compass rose here.
00:11
The boat is traveling in the direction of south, but then rotates 65 degrees to the west.
00:17
So it's traveling like this, and this angle right here is 65 degrees.
00:24
Okay, that's our first vector.
00:26
And this is going at 25 miles per hour.
00:32
Okay, it hits a current traveling at six miles per hour in the direction of north 15 degrees to the west.
00:42
So that vector, if we think of north and then rotating like this, 15 degrees to the west and this is eight miles per hour.
00:56
So there's my vectors my to think of them these two vectors and we want to find the magnitude and the direction of the boat so to do that i got to put them i'm going to use the tail the tip method so i'm going to take my purple vector right here which is 8 miles per hour and i'm going to slide it down and i'm going going to put it on the tip its tail on the tip of the red vector which is 25 miles per hour okay and then our resulting vector will make it this black one is this this one right here it's black one okay so now how in the world are we going to find find figure out what this these angles are we got to figure out all these angles all right so who knows don't know all right here's the thing you gotta remember these angles are all or these vectors are all parallel to each other remember this this purple vector was originally drawn on, like right, it was originally right here, okay, and if we think about back to our, i'll put in green now, so our compass rose looks like this, right, this angle right here was 15, this angle here was 65, if i slide the whole thing, if i slide the whole thing down here, here's my compass rose, rose, that's my north -south line, so to speak, right? okay, this angle right here would have to be 65 degrees because it's, with the red line, they're alternate interior angles of each other.
03:03
This angle over here is 15 degrees because it's the same.
03:09
They're, again, they're actually, what are they? you have two sets of parallel lines.
03:16
I just moved, i just slid this whole thing down to right here, okay? so the 65 is an alternate interior angle.
03:24
This 15 degree angle just moved to here.
03:27
All right, let me get rid of all this stuff i just wrote.
03:30
Okay, so that tells us, as i get rid of everything so i can write it in, that the angle at where the red vector meets the the purple vector is 65 plus 15 or 80 degrees right there.
03:49
And there we go.
03:50
That is the big thing we needed right there.
03:53
Because now if i want to find the magnitude here of this vector right here, i could use the law of cosines.
04:06
So x squared, i'm calling it x, the magnitude.
04:10
Of the, so that's the magnitude of our resultant vector.
04:15
X squared is going to equal 8 squared plus 25 squared minus 2 times 8 times 25 times the cosine of that 80 degrees i found right there.
04:31
This all has to be done in one step.
04:34
So we have 64 plus 625 minus, make sure your calculator is in degree mode.
04:42
The cosine of 80 is a positive number.
04:46
So cosine of 80, if i hit the buttons correctly, it'll be good.
04:51
And i'm going to times that by 2 and by 8 and by 25...