WAEC 2019 · Paper 2 · Q15

(a)
A body of mass $4\text{ kg}$ placed at the top of a smooth plane inclined at an angle of $35^\circ$ to the horizontal slides from rest down the plane. If the plane is $300\text{ m}$ long, calculate, correct to two significant figures, the speed of the body when it has travelled half the length of the plane. $[\text{Take } g = 10\text{ m s}^{-2}]$
(b)
An object falling from a tree passes through points $P$ and $Q$ with speeds $5.5\text{ m s}^{-1}$ and $30.5\text{ m s}^{-1}$ respectively. Find the: (i) distance $PQ$ ; (ii) average speed of the object while falling from $P$ to $Q$ . $[\text{Take } g = 10\text{ m s}^{-2}]$
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

The plane is smooth: $a = g\sin35^\circ$
$= 10 \times 0.5736$
$= 5.736\text{ m s}^{-2}$ down the plane.
Half the plane is $150\text{ m}$ : $v^2 = 0 + 2(5.736)(150) \approx 1720.7$ .
$v \approx 41\text{ m s}^{-1}$ (2 s.f.).

$v^2 = u^2 + 2gs$ : $30.5^2 = 5.5^2 + 20s$ , so $s = \dfrac{900}{20} = 45\text{ m}$ .