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WAEC 2011 · Paper 2 · Q5

  1. (a)

    Write the following as column vectors: r=(10 N,090∘)\mathbf r = (10\text{ N}, 090^\circ); q=(8 N,135∘)\mathbf q = (8\text{ N}, 135^\circ).

    Separate values with commas, e.g. 3, −2

  2. (b)

    Use your answer in (a) to find (r+q)(\mathbf r + \mathbf q).

    Separate values with commas, e.g. 3, −2

Worked solution (try it first)
  1. For a force (F,θ)(F, \theta) on a bearing, the column vector is (Fsin⁡θFcos⁡θ)\begin{pmatrix} F\sin\theta \\ F\cos\theta \end{pmatrix} (east on top, north below).

(a)

  1. r=(10sin⁡90∘10cos⁡90∘)\mathbf r = \begin{pmatrix} 10\sin90^\circ \\ 10\cos90^\circ \end{pmatrix}
    =(100)= \begin{pmatrix} 10 \\ 0 \end{pmatrix}.
  2. q=(8sin⁡135∘8cos⁡135∘)\mathbf q = \begin{pmatrix} 8\sin135^\circ \\ 8\cos135^\circ \end{pmatrix}
    =(42−42)= \begin{pmatrix} 4\sqrt2 \\ -4\sqrt2 \end{pmatrix}
    ≈(5.66−5.66)\approx \begin{pmatrix} 5.66 \\ -5.66 \end{pmatrix}.

(b)

  1. r+q=(10+42−42)\mathbf r + \mathbf q = \begin{pmatrix} 10 + 4\sqrt2 \\ -4\sqrt2 \end{pmatrix}
    ≈(15.66−5.66)\approx \begin{pmatrix} 15.66 \\ -5.66 \end{pmatrix}.

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