WAEC 2017 · Paper 2 · Q14

(a)
A body $P$ of mass $q\text{ kg}$ is suspended by two light inextensible strings $AB$ and $DB$ attached to a horizontal ceiling. The strings are inclined at $30^\circ$ and $60^\circ$ respectively to the horizontal and the tension in $AB$ is $48\text{ N}$ . If the system is in equilibrium: (i) sketch a diagram to represent the information; (ii) calculate the tension in $DB$ ; (iii) find the value of $q$ . $[\text{Take } g = 10\text{ m s}^{-2}]$
Separate values with commas, e.g. 3, −2
(b)
A ball is thrown vertically upwards with a velocity of $20\text{ m s}^{-1}$ . Find, correct to two decimal places, the: (i) maximum height reached by the ball; (ii) time taken to reach the maximum height. $[\text{Take } g = 10\text{ m s}^{-2}]$
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

Draw the body hanging from $B$ , with $AB$ at $30^\circ$ and $DB$ at $60^\circ$ to the ceiling, and its weight $10q$ downwards.

Across: $48\cos30^\circ = T\cos60^\circ$ .
$T = \dfrac{48\cos30^\circ}{\cos60^\circ}$
$= 48\sqrt3$
$\approx 83.14\text{ N}$ .