Babynini
  • Babynini
Magnitudes and directions of vectors.
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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Babynini
  • Babynini
The magnitudes and directions of two forces acting at a point p are given. Approximate the magnitude and direction of the resultant vector, accurate to two decimal places a) 5.00lb, 200 degrees b) 7.00lb, 65 degrees.
Babynini
  • Babynini
@jim_thompson5910 :P can we do this one?
jim_thompson5910
  • jim_thompson5910
|dw:1433465574025:dw|

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jim_thompson5910
  • jim_thompson5910
|dw:1433465584644:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1433465617485:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1433465663391:dw|
jim_thompson5910
  • jim_thompson5910
find the component form of each vector then you can add up the vectors component-wise
jim_thompson5910
  • jim_thompson5910
x = r*cos(theta) y = r*sin(theta)
Babynini
  • Babynini
Where do I derive the r from?
jim_thompson5910
  • jim_thompson5910
r = distance from origin to vector tip r = magnitude of vector (ie force applied)
Babynini
  • Babynini
so 5 for part a a) would be 5cos(200) 5sin(200) ?
jim_thompson5910
  • jim_thompson5910
yes
Babynini
  • Babynini
a = <-4.698,-1.710>
Babynini
  • Babynini
b= <2.958,6.344>
Babynini
  • Babynini
and when I add those up I get = <-1.74,4.63>
jim_thompson5910
  • jim_thompson5910
they want it "accurate to two decimal places"
Babynini
  • Babynini
...that's what I did o.0
Babynini
  • Babynini
oh, I didn't do a and b accurate to two decimal places but that's because that's part of the process to get to the final answer and should be more accurate I think (hence more decimal places) but the final answer is ok, yeah?
jim_thompson5910
  • jim_thompson5910
hmm maybe they just want the final answer to 2 decimal places, the steps just leave it to 15 or so (let the calculator handle it)
Babynini
  • Babynini
haha k. final answer looks good though? :)
jim_thompson5910
  • jim_thompson5910
yes it looks perfect. I'm getting the same
jim_thompson5910
  • jim_thompson5910
oh wait
jim_thompson5910
  • jim_thompson5910
they don't want the form of the resultant they want the "magnitude and direction of the resultant vector"
Babynini
  • Babynini
ou.
jim_thompson5910
  • jim_thompson5910
r = magnitude theta = direction r = sqrt(x^2 + y^2) theta = arctan(y/x) will give you the angle, but it will say some angle in Q4. Add on 180 degrees to move the angle to Q2 = <-1.74,4.63> is in Q2
Babynini
  • Babynini
so magnitude: 4.95
jim_thompson5910
  • jim_thompson5910
yes
jim_thompson5910
  • jim_thompson5910
|dw:1433466781150:dw|
Babynini
  • Babynini
theta = 110.58
jim_thompson5910
  • jim_thompson5910
nvm, my drawing is way off and not to scale
jim_thompson5910
  • jim_thompson5910
the "7 lb" vector should be longer, that's probably why
Babynini
  • Babynini
It's all good.
jim_thompson5910
  • jim_thompson5910
I'm getting roughly the same theta
Babynini
  • Babynini
haha yeah just a little disproportional xD
Babynini
  • Babynini
have you been rounding? I have been using calculator storages
jim_thompson5910
  • jim_thompson5910
I got 110.581677969387
Babynini
  • Babynini
yep yep :) same.
Babynini
  • Babynini
So final answer is The magnitude : 4.95 The direction = 110.58
jim_thompson5910
  • jim_thompson5910
yes
Babynini
  • Babynini
Fantastic! I like this question better than the car one heh
jim_thompson5910
  • jim_thompson5910
yeah much easier
Babynini
  • Babynini
For sure

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