How do I find the vertical component of a vector?

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How do I find the vertical component of a vector?

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Answer 1 · 2014-08-19T12:39:52

The formula for the vertical component of a vector ai + bj is as follows:

$v_y = ||A|| sin(θ)$

First, calculate the magnitude of the vector A which is $||A||$ :
||A|| = $sqrt(a^2 + b^2)$

Next, determine $theta$
If you draw a triangle where a is the x axis and b is the y axis, you get a right triangle. The angle $theta$ has the following measurement below:
$tan(theta) = b/a$
$theta = artcan(b/a)$

Finally, we have the vertical component formula:
$v_y = ||A|| sin(θ)$

For calculator assistance, use the component button here:

http://www.mathcelebrity.com/vector.php

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How do I find the vertical component of a vector?

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