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Apologia physics M3
Two-dimensional vectors
Question | Answer |
---|---|
two-dimensional motion | motion that occurs in a plane |
displacement | when you are given both a distance and a direction |
magnitude | the length of an arrow in a 2 D vector |
arrows | represent 2-dimensional vectors |
direction | where the arrow points |
the direction of the vector | the angle between the arrow and the positive x-axis |
tangent of an angle (tan) | in a right triangle, the opposite side from an angle divided by the adjacent side (opposite over adjacent) |
cosine of an angle (cos) | in a right triangle, the adjacent leg divided by the hypotenuse (adjacent over hypotenuse) |
sine (sin) | in a right triangle, the leg opposite the angle divided by the hypotenuse (opposite over hypotenuse) |
inverse tangent | useful when we have the tangent of an angle, but not the angle itself; can be used to determine the measure of an angle |
direction is always defined | relative to the positive x-axis |
When adding vectors graphically, | take the tail of the second vector and place it at the head of the first vector. |
You can move a vector | anywhere you want, as long as you do not change its magnitude (length) or direction (angle relative to the x-axis). |
When subtracting vectors, | take the vector being subtracted and make it point precisely in the opposite direction. Then add that vector to the first. |
The x-component of a vector tells us | how far along the x-axis you traveled to get to the destination. |
The y-component of a vector tells us | the distance you had to travel in the y-direction |
All two-dimensional vectors have | x- and y- components. |
In order to keep all of our vectors consistent, | physicists like to always define the angle of a vector starting at the positive x-axis. |
If your x- and y-components are both positive, | the vector must be in region one and is properly defined. |
If your x-component is negative and your y-component is positive, | the vector must be in region II and you need to add 180 degrees to your calculator's answer. |
If your x-component and y-component are both negative, | the vector must be in region III and you need to add 180 degrees to your calculator's answer. |
If x-component is positive and your y-component is negative, | the vector must be in region IV and you need to add 360 degrees to your calculator's answer. |