WAEC 2008 · Paper 2 · Q8✱✱

The magnitude of a force $x\mathbf i + 15\mathbf j$ is $17\text{ N}$ .

(a)
Find the possible values of $x$ .
Separate values with commas, e.g. 3, −2
(b)
Find the directions of the forces, correct to the nearest degree.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

For $8\mathbf i + 15\mathbf j$ : the force points up (north) and to the right (east).
Its angle from north is $\tan^{-1}\frac{8}{15}$ .
$\tan^{-1}\frac{8}{15} \approx 28.07^\circ$ , so the direction is $\text{N}28^\circ\text{E}$ , a bearing of $028^\circ$ .
For $-8\mathbf i + 15\mathbf j$ : the force points north and to the left (west), at the same $28^\circ$ from north.
Its direction is $\text{N}28^\circ\text{W}$ , a bearing of $360^\circ - 28^\circ = 332^\circ$ .