Math

A force of magnitude 15 N is the resultant of two forces, one of which has a magnitude of 8 N and acts at an angle of 30° to the resultant. Find the magnitude and direction of the other force.

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  1. You just need to solve a triangle. The other force z
    |z|^2 = 8^2 + 15^2 - 2*8*15 cos30° = 81.15
    |z| ≈ 9
    z makes an angle θ with the resultant, where
    8^2 = |z|^2 + 15^2 - 2*|z|*15*cosθ
    θ = 26.36°, but points toward the resultant, so θ = -26.36°

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  2. or, let the resultant v be aligned with the x-axis. Then
    v = (15,0)
    and the other force u = (6.93,4.00)
    So, you want z=(x,y) such that
    (x+6.93) = 15
    (y+4.00) = 0
    z = (8.07,-4.00)
    |z| = 9.01
    tanθ = y/x = -4/9
    θ = -23.94°
    Hmmm. I guess I was a bit off above, eh?
    Well, you can double-check my work and see which is correct.

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