Answers:
Magnitude of force P = 163.041494
Magnitude of resultant force = 184.320997
Values are approximate. Units are in newtons.
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Step-by-step explanation:
Let for P be pulled directly to the east. The vector for this force is <x, 0> where x is positive.
The 200 newton force has the vector <200*cos(120), 200*sin(120)>
The resultant vector is <x+200*cos(120),200*sin(120)>. Each component is the sum of the corresponding components of <x,0> and <200*cos(120), 200*sin(120)>
The resultant vector is also <r*cos(70),r*sin(70)>. Note how 70+50 = 120. The 50 degree angle is known, so we effectively do 120-50 = 70 to find the angle of the resultant vector with the positive x axis.
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The resultant vector expressions we found were
- <r*cos(70),r*sin(70)>
- <x+200*cos(120),200*sin(120)>
Equate the y components of each resultant vector expression. Solve for r
r*sin(70) = 200*sin(120)
r = 200*sin(120)/sin(70)
r = 184.320997021376
Make sure your calculator is in degree mode.
Let's round this r value to 6 decimal places to simplify things a bit
r = 184.320997
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Now equate the x components of each resultant vector expression, plug in the r value we found, and solve for x
x+200*cos(120) = r*cos(70)
x+200*cos(120) = 184.320997*cos(70)
x = 184.320997*cos(70) - 200*cos(120)
x = 163.041494
this value is approximate just like r is as well
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The magnitude of force P is
magnitude = sqrt(x^2+y^2)
magnitude = sqrt(x^2+0^2)
magnitude = sqrt((163.041494)^2+0^2)
magnitude = 163.041494
Which is equal to the x value. This applies because y = 0.
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The magnitude of the resultant is r = 184.320997 which we found earlier