WAEC 2016 · Paper 2 · Q15

(a)
Given that $\mathbf m = 6\mathbf i + 8\mathbf j$ and $\mathbf n = -8\mathbf i + \frac73\mathbf j$ , find, correct to two decimal places, the magnitudes and directions (bearings) of $\mathbf m$ and $\mathbf n$ .
Show the answer
$|\mathbf m| = 10.00$ on $036.87^\circ$ ; $|\mathbf n| = 8.33$ on $286.26^\circ$
(b)
A car travelling at $30\text{ m s}^{-1}$ is brought to rest in a distance of $50\text{ m}$ . Calculate: (i) its acceleration; (ii) the time taken for it to come to rest.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

$|\mathbf m| = \sqrt{36 + 64} = 10.00$ .
$\mathbf m$ points 6 east and 8 north: $\tan^{-1}\frac68 = 36.87^\circ$ from north, a bearing of $036.87^\circ$ .
$|\mathbf n| = \sqrt{64 + \frac{49}{9}}$
$= \sqrt{\frac{625}{9}}$
$= \frac{25}{3}$
$\approx 8.33$ .
$\mathbf n$ points 8 west and $\frac73$ north: $\tan^{-1}\frac{8}{7/3} = 73.74^\circ$ west of north.
So the bearing is $360^\circ - 73.74^\circ = 286.26^\circ$ .