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Components of Vectors

Teacher/Instructor Matt Jones
Matt Jones

M.Ed., George Washington University
Dept. chair at a high school

Matt is currently the department chair at a high school in San Francisco. In his spare time, Matt enjoys spending time outdoors with his wife and two kids.

Two-dimensional vectors have two components: an x vector and a y vector. Each of these vector components is a vector in the direction of one axis. The sum of the components of vectors is the original vector. Three-dimensional vectors have a z component as well.

Okay let's look at some components of vectors, if I have a vector let's say I've got 40 meters per second and it's going at 35 degrees above the horizon okay if I'm not going totally horizontal or totally vertical I can really break this vector down into 2 vectors. 1 along the x axis and 1 along the y axis. So this is often useful in Physics, so let's go ahead and do that I can say this vector is going to equal my x vector which I'm just going to call vx velocity in the x direction and a y vector which I'm going to call vy the velocity in the y direction.

Okay, so if I've got this going 40 meters per second in 35 degrees above the x axis what is my x and y velocities? How can I convert that and to do that I've got to do a Trigonometry okay because really I can calculate this velocity if I have this velocity and this angle and I have a right triangle okay by saying that the velocity x is equal to the initial velocity times the cosine of theta and in this case theta is 35 degrees. Okay if we go ahead and plug in the cosine of 35 degrees is 0.8191 and multiply that by our 40.0 meters per second we get 32.76 meters per second.

Okay now is that okay, is that perfect? Well if we want to go with significant figures we have 3 significant figures in our initial value right there so let's go ahead and convert that to v of x equals 32.8 meter per second. Okay so my vx=32.8 meters per second. Okay now let's look at the y vector okay in this case my y vector when I compare it to the v1 okay I can calculate that by saying my vector y equals my initial vector times the sine of theta remember sine is the relationship between this and this, this side and this side.

Okay in this case the sine of 35 degrees is 0.5735 and I multiply that by 40 meters per second I get 22.94 meters per second okay, and again knowing that I have 3 significant figures in my initial value let's calculate the vy into 22.9 meters per second and this equals 22.9 meters per second. Okay so what we've don here is we've taken 1 vector and broken it down into it's x and y components in this case the velocity in an angle equals the velocity in x and the velocity in y.