resultant vector calculation

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resultant vector calculation

Postby Integr88 » Fri 08 April, 2011 13:09

here is I have one vector with magnitude 7 and 30 degrees and the other with magnitude of 3 and angle of 90 degrees.
how can I find the resultant vector?
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Re: resultant vector calculation

Postby barnamah » Fri 08 April, 2011 13:27

If we have one vector `7/_30` and the other `3/_90` how can I calculate the resultant vector?

in `7/_30` we see that hypatenous is 7 and angle is 30degrees so to find the y side
`sin30=y/7` solving for y by multiplying both side by 7 we get: `y=7sin30=7/2`

as we know for vector we arrange them tip to toe so the `3/_90` will come on top of the `7/_30` because it is 90 degrees and it is vertical which creates a longer y s:
the new `y=7/2 +3=13/2`

so `y_2=13/2`

Now we can use similar triangle to calculate. We have:
Triangle 1: 30 degrees with `y_1=7/2`
Triangle 2: unknown degree x with `y_2=13/2`

`30/(7/2)=x/(13/2)` doing cross multiplying we have:
`7/2x=30(13/2)` so `x=(30(13/2))/(7/2)=55.7`

so the angle is 55.7 degrees

`:.` the resultant vector has magnitude of 13/2 and 55.7 degree `13/2/_55.7^o`
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