00:01
So we have an airplane that's traveling 600 kilometers per hour and going south, 30 degrees east.
00:07
And so we know that south, 30 degrees east, and so i make magnitude is 600.
00:16
And we know that this is the 30 degree angle.
00:19
This is the 60 degree angle.
00:20
So if i draw a vertical line up, i can get my components.
00:26
30 -60 -90 triangle, half of the hypotenuse is how long this side.
00:30
Will be and if we take the east leg times square root of three that's how long this side is so we end up having the i component as 300 and the j component as negative 519 .62 to two decimal places now likewise we can work with the wind and the wind was south 45 degrees east and it was only 40 kilometers and i could have drawn it right here head to tail and done a little bit of trig to find this out with law of cosines but let's just change this again into its uh into the i j components and we have for this one with a 45 45 90 triangle that if we take the hypotenuse divided by square root of two we find out how long that leg is so i did that division and we have a positive eye component and a negative j component just like the other.
01:31
So the resultant vector adding the i components, adding the j components, there is our resultant vector in the ij form.
01:42
Now it's speed using pithagorean theorem...