00:01
Hi there, so for this problem, we are told that a person is walking following the paths that i'm shown in this figure.
00:10
So this trip consists of four straight lines, and at the end of this walk, the persons want to know the result on displacement that is measured from the starting point.
00:27
So, as you can see from the figure, the straight path are given by vectors.
00:36
So we can obtain the resultant vector from this or the resultal displacement of this, but just summing all of the displayment.
00:46
We're going to call this the vector d1, this the vector d2, this the vector d3, and finally this the vector d4.
00:58
So we need to sum all of those vectors in order to get the resulting vector.
01:14
So the first thing that we need to write is all of these vectors.
01:20
So we're going to use a unit vector notation so that we will have.
01:27
For the vector d1, we can see that it only has x components.
01:34
So it should be 100 meters, that's the magnitude of the displacement, times the in the direction y and the direction i, because that gives us the direction in the x component.
01:51
So that's it for the displacement one.
01:54
Now for the displacement two, we will have only one component again, but in this case is in the y component.
02:01
As you can see, it is vertical.
02:06
So we will have that in this case is minus because it's pointing downward.
02:12
So it is minus 300 meters.
02:17
That's the magnitude of this vector.
02:23
In the j direction, because j is the unit vector for the y component.
02:29
Now that is it for this part of the problem.
02:33
Now for the vector 3, there is something more difficult because that vector has two components, an x company and a y component.
02:46
As you can see, the angle that it makes is with the horizontal.
02:59
So if we move or access to here, we can see that both components are, are going to be negative.
03:08
So for the ad company, we will have the magnitude that is minus, because it's pointing to the left.
03:16
It is 150 meters in the ed's component.
03:22
And for the white component, also sorry i forgot, that that component, because the angle is with respect to the horizontal, that component is given by the cosine of 30 degrees.
03:35
And this is the, component.
03:38
Now for the y component we are given that seems the vector is pointing downward we will have that this is also minus but in this case is 150 meters times the sign of 30 degrees and this in the j component.
03:56
Now for the final vector default we are going to have the following we can see that the vector is pointing to the left that means an m negative x component, but upward, that means a positive white component.
04:16
So for that information, we can have that is 1 ,200 meters, the minus 200 meters, and in this case, again, the angle is given by, and with respect to the horizontal, so that is by given by the cosine of 60 degrees in the x component.
04:43
And the y component, as i said, since the battery is pointing upward, this is going to be positive and it is the magnitude times the sign of 60 degrees in the y component.
05:01
So what we can do is to sum all of these components.
05:05
Separately.
05:07
So, well, i'm going to multiply this so you can have an explicit number.
05:15
So for d3, when we plot this into the calculator, we obtain that.
05:20
The x component is minus 130 meters in the x component, and the white component is minus 75 meters.
05:34
Now for the, um, vector t4 we have minus 100 meters in the x component and 173 meters in the y component.
05:56
So with this information, we can obtain the resultant force.
06:00
We're going to first sum all of the x component of this.
06:07
So we will have this x component, well, this is not the s component here.
06:13
So for d1, we only have an x component, so that is 100 meters.
06:21
The vector d2 has no an x component, so we don't need to sum that...