## TrojanPoem one year ago Mechanics

1. TrojanPoem

@phi

2. Jack1

what specifically about mechanics? do u have an engineering based question?

3. TrojanPoem

Nah, general question.

4. TrojanPoem

Are you an engineer ?

5. phi

|dw:1444139335225:dw|

6. Jack1

nah, just ok at maths

7. phi

if we use the Law of Cosines on that triangle |dw:1444139454924:dw|

8. TrojanPoem

That's why I was getting the wrong angles -,-

9. phi

x is the angle between u and v but in the triangle the "opposite angle" is 180 - x cos (180-x) = - cos(x)

10. 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)

11. TrojanPoem

How ? It wasn't clear 131 ? on the last question

12. phi

Using the Law of Cosines idea? |dw:1444139889064:dw|

13. TrojanPoem

|dw:1444139666557:dw|

14. TrojanPoem

Why isn't 180 - Alpha = alpha ? Symmetry

15. phi

alpha (apparently, based on the answer choices) is the angle between v and f the angle between u and v is alpha + theta

16. TrojanPoem

|dw:1444140291240:dw|

17. phi

yes. with theta= 40, you get 120-alpha now it will work

18. phi

*140 - alpha

19. TrojanPoem

300/ sin alpha = 256.9 / sin40 sinalpha^-1 = 48.64 -,-

20. TrojanPoem

What am I doing wrong ?

21. phi

I think it would help if you drew a picture that more closely matched the situation

22. TrojanPoem

|dw:1444140790074:dw| That's our start then |dw:1444140826725:dw| then using the sine rule.

23. 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

24. phi

|dw:1444141166027:dw|

25. 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

26. TrojanPoem

Using vectors'd give me the answer directly, however, I've to answer this question using cosine / sine rule :/

27. phi

the other way around the ambiguity is choose the acute angle rather than alpha

28. TrojanPoem

140 - alpha ?

29. TrojanPoem

Alpha doesn't seem like an obtuse in the drawing :/

30. phi

|dw:1444141658047:dw|

31. TrojanPoem

Fine, thanks phi :)

32. phi

$\frac{\sin (140-\alpha)}{60}= \frac{\sin(40)}{256.9}$

33. TrojanPoem

Phi, I noticed that 256.9 is out of the choices -,-

34. TrojanPoem

a)112.7 b ) 145.9 c) 154.3 d ) 257.9

35. TrojanPoem

@phi

36. phi

Yes, I noticed that before. I assume it is a typo. Here are the 3 vectors

37. TrojanPoem

Ok, as you're sure.

38. phi

You can ask your teacher, but the numbers work out to 256.9

39. TrojanPoem

Yeah, 257.9 works too with 131.4

40. TrojanPoem

u+v= f so v= f-u f=<300,0> (we let f point along the x-axis u= 60<cos 40, -sin 40> 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.

41. phi

Yes, I'm sure the magnitude is 256.9 But complain to your teacher.

42. TrojanPoem

I will.