Thread: 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.

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) .

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?

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 , where and 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 . Neither of the components of this given vector is 100. Its length is 100.