00:01
In this problem, we're going to use the concept of vector sum.
00:04
So suppose that we have two vectors, a and b, and a can be written as ax times i plus ay times j, while b is bxi plus byj.
00:23
And if we want to sum these two vectors, all we do is sum the component by component.
00:33
To be a x plus bx i plus a y plus b y j okay uh and also one thing that's going to be useful for us is if we have a vector and we have the magnitude of the vector let's say that the magnitude is v and we have the angle it makes with a horizontal and we want to transform this into a component notation then we can set up a coordinate system.
01:09
So let's say that the y -axis points upwards, the x -exus points to the right.
01:16
So the vector of v will be the magnitude of the vector times the cosine of theta i plus the magnitude of the vector times the sine of theta j.
01:31
This is what we're going to need in our exercise.
01:35
So what we have is a car that starts at the origin of our coordinate system so i'm gonna just draw a coordinate system here and the car starts at the origin and then drives 1 .2 kilometers directly to the south so 1 .2 kilometers.
01:58
Then the car drives 3 .1 kilometers to the north -east making an angle such that it's 53 degrees north of east.
02:15
Okay, as shown here, east is to the right.
02:19
North is upward, so this is 53 degrees north of east.
02:23
And our goal is to find what is the distance between the origin and the final point of the car, as well as the angle theta that this vector that connects the origin to the car makes with the horizontal.
02:47
Okay, so, and this is 3 .1 kilometers, i'd forgotten to write.
02:55
So this basically amounts to summing these two vectors, the vector that has a magnitude of 1 .2 kilometers and the one that has a magnitude of 3 .1 kilometers.
03:05
So i'm going to write both vectors in a component form.
03:10
So first vector, i'm going to call it a, and a only has a component in the y direction, in the negative y direction, so it's minus 1 .2j kilometers.
03:25
B, i'll call the second one b, has a magnitude of 3 .1 kilometers.
03:35
Then in the x direction, we have 3 .1 times cosine of 53, i plus 3 .1 times the sign of 53j.
03:47
So b is equal to 1 .87 i plus 1 .28 j...