Solution 9.2c
From Mechanics
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}