Mechanics

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what specifically about mechanics? do u have an engineering based question?
Nah, general question.

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Other answers:

Are you an engineer ?
  • phi
|dw:1444139335225:dw|
nah, just ok at maths
  • phi
if we use the Law of Cosines on that triangle |dw:1444139454924:dw|
That's why I was getting the wrong angles -,-
  • phi
x is the angle between u and v but in the triangle the "opposite angle" is 180 - x cos (180-x) = - cos(x)
  • phi
a picture drawn to scale is very helpful. (If done very accurately, you can measure the answer), but even a rough drawing gives a good estimate of the answer (i.e. angle and length of the vector)
How ? It wasn't clear 131 ? on the last question
  • phi
Using the Law of Cosines idea? |dw:1444139889064:dw|
|dw:1444139666557:dw|
Why isn't 180 - Alpha = alpha ? Symmetry
  • phi
alpha (apparently, based on the answer choices) is the angle between v and f the angle between u and v is alpha + theta
|dw:1444140291240:dw|
  • phi
yes. with theta= 40, you get 120-alpha now it will work
  • phi
*140 - alpha
300/ sin alpha = 256.9 / sin40 sinalpha^-1 = 48.64 -,-
What am I doing wrong ?
  • phi
I think it would help if you drew a picture that more closely matched the situation
|dw:1444140790074:dw| That's our start then |dw:1444140826725:dw| then using the sine rule.
  • phi
as you know the Law of Sines is ambiguous when you have an obtuse angle notice sin(131.4)= sin(48.6) In this problem, you have to recognize you should choose the 131.4
  • phi
|dw:1444141166027:dw|
  • phi
V almost doubles back on u, and we have an obtuse angle opposite the longest side = 300 Considering these subtleties, perhaps using components (of vectors) is more straightforward
Using vectors'd give me the answer directly, however, I've to answer this question using cosine / sine rule :/
  • phi
the other way around the ambiguity is choose the acute angle rather than alpha
140 - alpha ?
Alpha doesn't seem like an obtuse in the drawing :/
  • phi
|dw:1444141658047:dw|
Fine, thanks phi :)
  • phi
\[ \frac{\sin (140-\alpha)}{60}= \frac{\sin(40)}{256.9}\]
Phi, I noticed that 256.9 is out of the choices -,-
a)112.7 b ) 145.9 c) 154.3 d ) 257.9
  • phi
Yes, I noticed that before. I assume it is a typo. Here are the 3 vectors
1 Attachment
Ok, as you're sure.
  • phi
You can ask your teacher, but the numbers work out to 256.9
Yeah, 257.9 works too with 131.4
u+v= f so v= f-u f=<300,0> (we let f point along the x-axis u= 60 v= <60 cos(40) - 300, -60 sin(40) > now find the magnitude and angle of v |v| = 256.9 angle = atan(y/x) = 8.6 deg in the 3rd quadrant= 171.4 alpha = 171.4-40= 131.4 deg maybe it's a typo we've two solutions here which come with the same result.
  • phi
Yes, I'm sure the magnitude is 256.9 But complain to your teacher.
I will.

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