Solution 9.2c

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The sum of the forces is zero as the body has constant velocity. This means the sum of the forces in all directions is zero.

Resolving horisontally,

\displaystyle \begin{align} & \to :\quad 42\cos {{30}^{\circ }}+P-Q\cos {{45}^{\circ }}=0 \\ & \\ \end{align}

Resolving vertically,

\displaystyle \begin{align} & \uparrow :\quad 25+42\sin {{30}^{\circ }}-Q\cos {{45}^{\circ }}=0 \\ & \\ & Q=\frac{25+42\sin {{30}^{\circ }}}{\cos {{45}^{\circ }}}=\frac{46}{0\textrm{.}707}=65\textrm{.}1 \ \text{N} \\ \end{align}

Substituting this value for \displaystyle Q in the first equation gives

\displaystyle P=Q\cos {{45}^{\circ }}-42\cos {{30}^{\circ }}=65\textrm{.}1\times 0\textrm{.}707-42\times 0\textrm{.}866=46-36\textrm{.}4=9\textrm{.}6\ \text{N}