Mathematics 9709 · AS & A Level · Forces and equilibrium

Forces and equilibrium — practice question

At point O, which is the origin of the x-axis and y-axis, three horizontal forces of magnitudes $F\,\text{N}$, $63\,\text{N}$ and $25\,\text{N}$ are acting. These forces are in equilibrium. The force with magnitude $F\,\text{N}$ is inclined at an angle $\theta$ anticlockwise to the positive $x$-axis. The force of magnitude $63\,\text{N}$ is directed along the negative $y$-axis. The force of magnitude $25\,\text{N}$ is directed at $\tan^{-1}0.75$ clockwise from the negative $x$-axis (see diagram).
(main)[5]

Find the value of $F$ and the value of $\tan\theta$.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: Resolve $F$ into its $x$-component and $y$-component

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