WAEC 2014 · Paper 2 · Q15

(a)
$PQRS$ is a square. Calculate the magnitude and direction of the resultant of the forces $5\text{ N}$ acting along $PQ$ , $3\sqrt2\text{ N}$ acting along $PR$ and $3\text{ N}$ acting along $PS$ .
Separate values with commas, e.g. 3, −2
(b)
A book of mass $0.8\text{ kg}$ is placed on a plane inclined at $30^\circ$ to the horizontal. Find the frictional force if the book: (i) does not slide; (ii) slides with an acceleration of $1.2\text{ m s}^{-2}$ . $[\text{Take } g = 10\text{ m s}^{-2}]$
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

Take $PQ$ and $PS$ as the two directions.
$PR$ is the diagonal, at $45^\circ$ to each.
Along $PQ$ : $5 + 3\sqrt2\cos45^\circ = 5 + 3$
$= 8\text{ N}$ .
Along $PS$ : $3 + 3\sqrt2\sin45^\circ = 3 + 3$
$= 6\text{ N}$ .
$R = \sqrt{8^2 + 6^2} = 10\text{ N}$ , at $\tan^{-1}\frac68 \approx 36.9^\circ$ to $PQ$ .