Physics

Vector A has a magnitude of 13.0 units and points due west. Vector B points due north.
(a) what is the magnitude of B if A+B has a magnitude of 16.8 units?
(b) What is the direction of A+B relative to due west?
(c) What is the magnitude of B if A-B has a magnitude of 16.8 units?
(d) What is the direction of A-B relative to due west?

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asked by Sarah
  1. a. X = A = -13 Units.
    Y = B = ?
    Z= A+B = 16.8 Units = Resultant.

    X^2 + Y^2 = Z^2
    (-13)^2 + Y^2 = 16.8^2
    Y^2 = 16.8^2 - (-13)^2 = 282.24 - 169 =
    113.24
    Y = 10.64 Units = B.

    b. Tan Cr = Y/X = 10.64/-13 = -0.81846
    Cr = -39.3o = Reference angle.
    C = -39.3 + 180 = 140.7o CCW = 39.3o N of W.

    c. B = Y = 10.64

    d. X = -13. Y = -10.64.
    Tan Cr = Y/X = -10.64/-13 = 0.81846
    Cr = 39.30o = Reference angle.

    C = 39.3 + 180 = 219.3o CCW. = 39.3o S of W.

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    posted by Henry

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