Zenmo
  • Zenmo
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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perl
  • perl
Did you attempt to make a force diagram?
Zenmo
  • Zenmo
|dw:1433812186168:dw|
Zenmo
  • Zenmo
Well, that is what I have so far.

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Zenmo
  • Zenmo
This involves the section of "Vectors in a plane."
perl
  • perl
correct so far
perl
  • perl
|dw:1433819768895:dw|
Zenmo
  • Zenmo
Ops, forgot to put a 60 in there. Now, I'm not sure what to do next.
perl
  • perl
The directions state that the magnitude of the resultant is 90 pounds.
perl
  • perl
If we call the resultant vector R then magnitude of R= sqrt( Rx^2 + Ry^2)
Zenmo
  • Zenmo
What is the magnitude of R= sqrt(Rx^2+Ry^2) formula/name called?
perl
  • perl
that comes from pythagorean theorem
perl
  • perl
the length of a vector is the length of the hypotenuse
perl
  • perl
|dw:1433820260557:dw|
Zenmo
  • Zenmo
Just to check, R= sqrt (Rx^2+Ry^2) is the same as C= sqrt (Ax^2+By^2) ?
perl
  • perl
yes
Zenmo
  • Zenmo
|dw:1433813159626:dw|
perl
  • perl
|dw:1433820470702:dw|
perl
  • perl
|dw:1433820609869:dw|
Zenmo
  • Zenmo
=\[2025+3600\cos^2t+5400cost+3600\sin^2=8100\]
Zenmo
  • Zenmo
is that the correct next step?
Zenmo
  • Zenmo
ops forgot to put the t for 3600sin^2t.
perl
  • perl
yes
perl
  • perl
we can simplify this by factoring out 3600 from sin^2 t and cos^2 t
perl
  • perl
$$\large {2025+3600\cos^2t+5400\cos t+3600\sin^2 t=8100 \\ 2025+3600( \cos^2t +\sin^2 t ) +5400\cos t=8100 \\2025+3600( 1) +5400\cos t=8100 } $$
Zenmo
  • Zenmo
\[5625+5400\cos t = 8100. ->5400\cos t =2475. ->\cos t =2475/5400. -> \cos t = .4583 -> arc \cos t = 62.7 degrees.\]
perl
  • perl
now solve for t, the angle
Zenmo
  • Zenmo
\[\cos t = 0.4583 -> \arccos t (0.4583)\]
Zenmo
  • Zenmo
= 62.7 degrees?
Zenmo
  • 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)?
perl
  • perl
if you need to find magnitude of a vector, then yes :)
Zenmo
  • Zenmo
Ok, thanks again. :D

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