- Babynini

Magnitudes and directions of vectors.

- chestercat

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- 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

@jim_thompson5910 :P can we do this one?

- jim_thompson5910

|dw:1433465574025:dw|

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## More answers

- jim_thompson5910

|dw:1433465584644:dw|

- jim_thompson5910

|dw:1433465617485:dw|

- jim_thompson5910

|dw:1433465663391:dw|

- jim_thompson5910

find the component form of each vector
then you can add up the vectors component-wise

- jim_thompson5910

x = r*cos(theta)
y = r*sin(theta)

- Babynini

Where do I derive the r from?

- jim_thompson5910

r = distance from origin to vector tip
r = magnitude of vector (ie force applied)

- Babynini

so 5 for part a
a) would be
5cos(200)
5sin(200)
?

- jim_thompson5910

yes

- Babynini

a = <-4.698,-1.710>

- Babynini

b= <2.958,6.344>

- Babynini

and when I add those up I get
= <-1.74,4.63>

- jim_thompson5910

they want it "accurate to two decimal places"

- Babynini

...that's what I did o.0

- 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

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

haha k. final answer looks good though? :)

- jim_thompson5910

yes it looks perfect. I'm getting the same

- jim_thompson5910

oh wait

- jim_thompson5910

they don't want the form of the resultant
they want the "magnitude and direction of the resultant vector"

- Babynini

ou.

- 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

so magnitude: 4.95

- jim_thompson5910

yes

- jim_thompson5910

|dw:1433466781150:dw|

- Babynini

theta = 110.58

- jim_thompson5910

nvm, my drawing is way off and not to scale

- jim_thompson5910

the "7 lb" vector should be longer, that's probably why

- Babynini

It's all good.

- jim_thompson5910

I'm getting roughly the same theta

- Babynini

haha yeah just a little disproportional xD

- Babynini

have you been rounding? I have been using calculator storages

- jim_thompson5910

I got 110.581677969387

- Babynini

yep yep :) same.

- Babynini

So final answer is
The magnitude : 4.95
The direction = 110.58

- jim_thompson5910

yes

- Babynini

Fantastic! I like this question better than the car one heh

- jim_thompson5910

yeah much easier

- Babynini

For sure

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