whats R?
A 3m south of east
B 3m north
C 3m 30 degrees north east
D 3m 50 degrees south west

- anonymous

whats R?
A 3m south of east
B 3m north
C 3m 30 degrees north east
D 3m 50 degrees south west

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- anonymous

what's the general question ? ^_^

- anonymous

whats R? Magnitude of R and direction of R.

- anonymous

how can we determine the magnitude of R and direction of R if there's no problem lol?

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## More answers

- anonymous

i can show you a sample of a previous problem and how it's done.

- anonymous

Nikolas Oman April 17 at 6:46pm
best way to resolve each vector into perpendicular components.
i = positive horizontal direction (to the right)
j = positive vertical direction (up)
A = -5 cos 65 i + 5 sin 65 j
B = 5 cos 50 i - 5 sin 50 j
C = -5 cos 45 i - 5 sin 45 j
R = A + B + C = (-5 cos 65 + 5 cos 50 - 5 cos 45) i + (5 sin 65 - 5 sin 50 - 5 sin 45) j
R = -2.435 i - 2.834 j
Now use the Pythagorean Theorem to get the magnitude:
Magnitude of R = √(2.435² + 2.834²) = 3.7 m
Direction of R = arctan(-2.834/-2.435) = 229.3° ... so that's 49.3° south of west

- anonymous

that's the question? :)

- anonymous

no thats another problem. question is whats the magnitude and direction of R if vectors are:
A 3m south of east
B 3m north
C 3m 30 degrees north east
D 3m 50 degrees south west

- anonymous

LOL >_< my bad, I thought those were the choices ^^"

- anonymous

lol no
do you know how to do it?

- anonymous

I'll give it a try? :)

- anonymous

tnx :)

- anonymous

np ^_^

- anonymous

remind me,
In the previous problem, A = -5 cos 65 i + 5 cos65 j < -- angles were given? or is that the general form

- anonymous

angles were given

- anonymous

how about for this problem?

- anonymous

A 3m south of east
B 3m north
C 3m 30 degrees north east
D 3m 50 degrees south west

- anonymous

this is all that's given

- anonymous

hmm, that means that you have to figure out the angles from the given

- anonymous

B is easy, 3 m north , angle = 90 degrees

- anonymous

hmm yea and A? 45 degrees?

- anonymous

since they haven't given you the angles, yes you can assume that A = 45 degrees

- anonymous

and now? how much is R?

- anonymous

all you've got to do is use the same way you've used in the previous question :)
I think your prob was trying to figure out the angles? right?

- anonymous

well it's not my homework :) it's my friends homework and I have no idea how to do it :)

- anonymous

lol >_<

- anonymous

Alright, let's try to solve it together ^_^

- anonymous

she solved it and got 2.79m 1.65 degrees north of east and she just wants to check if it's ok

- anonymous

so:
i = positive horizontal direction (to the right)
j = positive vertical direction (up)
then we can say the following :
A = 3 cos 45 - 3 sin 45
B = 3 sin 90
C = 3 cos 30 + 3 sin 30
D = - 3 cos 50 - 3 sin 50

- anonymous

yep i agree so far

- anonymous

now:
R = A + B + C
= (3 cos 45 - 3 sin 45 ) + (3 sin 90 ) + (3 cos 30 + 3 sin 30) + (-3 cos 50 - 3 sin 50)
= 0 + 3 + pi - 4.23
= 1.912

- anonymous

R= 3 cos 45 + 3 cos 30 - 3 cos 50)i + (3 sin 45 + 3 sin 90 + 3 sin 30 - 3 sin 50)j

- anonymous

lol, wait, I've messed it up

- anonymous

yeah, hold on :)

- anonymous

ok

- anonymous

R = 1.76 i - 3.32 j
I might have some calculation mistakes, it happens ^_^

- anonymous

so this is it?

- anonymous

\[R = \sqrt((1.76)^2 + (3.32)^2)\]
= 3.74 m

- anonymous

alright thank you so very much!

- anonymous

arctan = -62.07

- anonymous

np :)

- anonymous

thank you thank you
so her answer was wrong?

- anonymous

I'm not sure what was her answer lol , I just followed the steps and given :)

- anonymous

ok thank you!

- anonymous

np ^_^, but I'm not sure though ^^"

- anonymous

is there an online calculator where i could check this?

- anonymous

there's your hand-calculator? :)

- anonymous

i dont have it :/

- anonymous

can you calculate this for me please?
R = (3 cos 45 + 3 cos 30 - 3 cos 50)i + (-3 sin 45 + 3 sin 90 + 3 sin 30 - 3 sin 50)

- anonymous

I did lol, that's what I got, answer above

- anonymous

you can check with your calculator if you want :)

- anonymous

oh ok thank you again :)

- anonymous

lol, np ^_^

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