$A$ boy drops a ball from a cliff $122.5 \, m$ high.
Find:
$(i)$ How long does it take the ball to fall to the ground?
$(ii)$ How far does it fall in the first three seconds?
$(iii)$ How fast is it going at the end of three seconds?

(N/A) Given:
Distance travelled by the ball,$S = 122.5 \, m$
Initial velocity,$u = 0$
Acceleration,$a = g = 9.8 \, m s^{-2}$
$(i)$ If $t$ is the time taken by the ball to fall to the ground,then using the equation of motion $S = ut + \frac{1}{2}at^2$:
$122.5 = 0 \times t + \frac{1}{2} \times 9.8 \times t^2$
$122.5 = 4.9 \times t^2$
$t^2 = \frac{122.5}{4.9} = 25$
$t = \sqrt{25} = 5 \, s$
$(ii)$ Distance travelled by the ball in the first three seconds $(t = 3 \, s)$:
$S = ut + \frac{1}{2}at^2$
$S = 0 \times 3 + \frac{1}{2} \times 9.8 \times (3)^2$
$S = 4.9 \times 9 = 44.1 \, m$
$(iii)$ Velocity of the ball at the end of three seconds $(t = 3 \, s)$:
$v = u + at$
$v = 0 + 9.8 \times 3 = 29.4 \, m s^{-1}$