## Zenmo one year ago Find the angle between the forces given the magnitude of their resultant. (Hint: Write force 1 as a vector in the direction of the positive x-axis and force 2 as a vector at an angle theta with the positive x-axis. Force 1=45 pounds, Force 2=60 pounds, Resultant Force= 90 pounds.

1. perl

Did you attempt to make a force diagram?

2. Zenmo

|dw:1433812186168:dw|

3. Zenmo

Well, that is what I have so far.

4. Zenmo

This involves the section of "Vectors in a plane."

5. perl

correct so far

6. perl

|dw:1433819768895:dw|

7. Zenmo

Ops, forgot to put a 60 in there. Now, I'm not sure what to do next.

8. perl

The directions state that the magnitude of the resultant is 90 pounds.

9. perl

If we call the resultant vector R then magnitude of R= sqrt( Rx^2 + Ry^2)

10. Zenmo

What is the magnitude of R= sqrt(Rx^2+Ry^2) formula/name called?

11. perl

that comes from pythagorean theorem

12. perl

the length of a vector is the length of the hypotenuse

13. perl

|dw:1433820260557:dw|

14. Zenmo

Just to check, R= sqrt (Rx^2+Ry^2) is the same as C= sqrt (Ax^2+By^2) ?

15. perl

yes

16. Zenmo

|dw:1433813159626:dw|

17. perl

|dw:1433820470702:dw|

18. perl

|dw:1433820609869:dw|

19. Zenmo

=$2025+3600\cos^2t+5400cost+3600\sin^2=8100$

20. Zenmo

is that the correct next step?

21. Zenmo

ops forgot to put the t for 3600sin^2t.

22. perl

yes

23. perl

we can simplify this by factoring out 3600 from sin^2 t and cos^2 t

24. perl

$$\large {2025+3600\cos^2t+5400\cos t+3600\sin^2 t=8100 \\ 2025+3600( \cos^2t +\sin^2 t ) +5400\cos t=8100 \\2025+3600( 1) +5400\cos t=8100 }$$

25. Zenmo

$5625+5400\cos t = 8100. ->5400\cos t =2475. ->\cos t =2475/5400. -> \cos t = .4583 -> arc \cos t = 62.7 degrees.$

26. perl

now solve for t, the angle

27. Zenmo

$\cos t = 0.4583 -> \arccos t (0.4583)$

28. Zenmo

= 62.7 degrees?

29. Zenmo

Ok, that is the answer. Thanks! One small question, so dealing with these type of problems, this will always involve the Pythagorean Theorem of R=sqrt(Rx^2+Ry^2)?

30. perl

if you need to find magnitude of a vector, then yes :)

31. Zenmo

Ok, thanks again. :D