physics honors

You are given a vector in the xy plane that has a magnitude of 100.0 units and a y component of -50.0 units

(b) Assuming the x component is known to be positive, specify the vector which, if you add it to the original one would give a resultant vector that is 85.0 units long and points entirely in the -x direction.
Magnitude ?

Direction ?

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  1. Y = ver = -50 (given),

    X^2 + (-50)^2 = (100)^2,
    X^2 = 10000 - 2500 = 7500,

    X = hor = sqrt(7500) = 86.6,

    Vector to be added:
    -50 + Y = 0,

    Y = 50 added.

    86.6 + X = -85,

    X = hor = -85 - 86.6 = -171.6 added.

    tanA = Y/X = 50/171.6 = 0.2914,
    A = 16.24 deg.

    Magnitude = y / sinA = 50/sin16.24
    = 178.7

    Direction = 16.24 deg above WEST.

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  2. Correction:
    Direction = 16.24 deg NORTH of WEST.

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