Find components using only 1 vector and 1 angle

Hi, I'm trying to figure out the solution to this question:

"If a force has magnitude 100 and is directed 45° south of east, what are its components?"

I diagrammed it so that I have a the vector with magnitude 100 and the vector going south-east at 45°, and so far I can only tell that the components of the first vector are <100, 0>. Where do I go from here?

Thanks for your help.

Re: Find components using only 1 vector and 1 angle

Quote:

Originally Posted by

**bumpjump** Hi, I'm trying to figure out the solution to this question:

"If a force has magnitude 100 and is directed 45° south of east, what are its components?"

I diagrammed it so that I have a the vector with magnitude 100 and the vector going south-east at 45°, and so far I can only tell that the components of the first vector are <100, 0>. Where do I go from here?

Thanks for your help.

Use trigonometry to find x and y (your components) .

Re: Find components using only 1 vector and 1 angle

Quote:

Originally Posted by

**Also sprach Zarathustra** Use trigonometry to find x and y (your components) .

A quick google search says SOHCAHTOA only works for right triangles; this is equilateral since the given angle is 45 degrees. What trig function will give me the components of the unknown vector?

Re: Find components using only 1 vector and 1 angle

First, an equilateral triangle has angles of 60 degrees, not 45! Second, given any one angle, you can always construct a right triangle having that as one of its angles. Draw x, y coordinates and think of "east" to the right, "north" upward, so "west" to the left, "south" downward. An angle "45° south of east" is at 45 degrees below the positive x-axis (the line to the right). Draw a line at that angle, of length 1. Drop a perpendicular from the end of that line to the x-axis. Now do you see the right triangle?

" I have a the vector with magnitude 100 and the vector going south-east at 45°, and so far I can only tell that the components of the first vector are <100, 0>."

Are you clear on what "components" of a vector **are**? There is no vector here that has components <100, 0>. If a vector $\displaystyle \vec{v}= a\vec{i}+ b\vec{j}$, where $\displaystyle \vec{i}$ and $\displaystyle \vec{j}$ are the unit vectors in the directions of the positive x and y axes ("east" and "north" here) then the components of the vector are <a, b>. The **length** of that vector is $\displaystyle \sqrt{a^2+ b^2}$. Neither of the components of this given vector is 100. Its **length** is 100.