Question:

Graphically determine the resultant of the following three vector displacements:

- $24 \textrm{ m}$, $36^\circ$ north of east;
- $18 \textrm{ m}$, $37^\circ$ east of north; and
- $26 \textrm{ m}$, $33^\circ$ west of south.

Source: Giancoli, Douglas C., Physics: Principles with Applications, 7th Edition, 2014.

Quick Answer:

$26 \textrm{ m } 13^\circ \textrm{ N of E}$

## Comments

Hello. Sr. If I decompose in Ax and Ay y got different result can you tell me why. Please.

Hi joeotilio25, this problem is meant to check a students ability to plot vectors on graph paper in the correct direction, and add them together. If you reduced the vectors to components, then added the components together, I would bet that your answer is more precise than mine. If you have an answer that is a some length more than $15 \textrm{ m}$ and less than $30 \textrm{ m}$, then consider your answer correct. I followed the text book instructions to add them graphically, rather than use a calculator. There is a human error in plotting the length and direction for each arrow, and this happens three times, so the errors are compounding. Actually, the error compounds four times when you consider the error in the resultant, so don't be surprised of your answer differs from what's shown. The thing to learn from this video is how to plot vectors, and what it means, graphically speaking, to add three of them together.

Hello, I got a different answer for this question. I divided all the vectors into x and y components and used pythagorean theorem at the end to find the resultant vector. My answer is 22.53 km ( 22.53 degrees North of East ).

Hi chaegyunkang, that's a fair question that other's have had as well. I'll paste my response to another student's similar point: "this problem is meant to check a students ability to plot vectors on graph paper in the correct direction, and add them together. If you reduced the vectors to components, then added the components together, I would bet that your answer is more precise than mine. If you have an answer that is a some length more than 15 m and less than 30 m, then consider your answer correct. I followed the text book instructions to add them graphically, rather than use a calculator. There is a human error in plotting the length and direction for each arrow, and this happens three times, so the errors are compounding. Actually, the error compounds four times when you consider the error in the resultant, so don't be surprised of your answer differs from what's shown. The thing to learn from this video is how to plot vectors, and what it means, graphically speaking, to add three of them together."

All the best,

Mr. Dychko