A disoriented physics professor drives 3.25 km north, then 2.20 km west, and then 1.50 km south. Find the magnitude and direction of the resultant displacement, using the method of components. In a vector-addition diagram (roughly to scale), show that the resultant displacement found from your diagram is in qualitative agreement with the result you obtained by using the method of components.

Video transcript

Welcome back everybody. We have James driving a car and he drives north for 4. km. Then he drives west for 2.8. Then he drives South 4, 1.3 and we need to figure out the magnitude and direction of the displacement vector. Now, just for naming conventions, I'm going to name this vector, A, B and C. And our total displacement vector. I'm going to name our. Now R is going to have a form just as any two dimensional vector is of having an X component. R X times I plus a Y component IMEs J. Now what are our X and our Y. R X is just going to be the sum of the X components of the other vectors. And same thing with the Y component as it is the sum of the Y components of the other vectors. But what are the X and Y components of the other vectors? Well, let's work that out real quick. A travels straight north and it doesn't move left or right. So its X component is going to be zero and it's moving in the positive Y direction or 00.5 kilometers. So its Y component is 4.5 Or be it moves left 2.8. So that is going to be negative 2.8 for its x component and it's not moving up or down. So that'll be a zero for the y component or C not moving left to right. So it will have an X component of zero is moving straight down 1. kilometers. So it'll be negative 1.34, it's J component. Now let's go ahead and find our X and our Y r. X. Going to be zero minus 2.8 plus zero Equal to -2.8. Ry is going to be 4.5 plus zero minus 1.3. Equaling 3.2 R is negative 2.8 I plus 3.2. Okay, now that we have the X and Y component of our let's go ahead and find the magnitude and direction magnitude is going to be the square root of the summation of all the components squared. So we are going to have negative 2.8 squared plus 3.2 squared and the square root of that is going to equal 4.25. Now for data we are going to use the formula that the arc tangent of the Y component divided by the X component is equal to the to the y component is 3.2 divided by negative 2.8 and this is equal to 131.2 degrees counterclockwise from the positive X axis which gives us our final answer of D Thank you guys so much for watching. Hope this video helped. We will see you all in the next one