Question

When a cricket ball is thrown vertically upwards, it reaches a maximum height of 5 metres.
(i) What was the initial speed of the ball?
(ii) How much time is taken by the ball to reach the highest point? (g = 10 m s⁻²)

Answer 1

(i) Let initial velocity of the ball = u

Final velocity of the ball = 0 m/s

The maximum height reached by the ball = 5 m

Acceleration of the ball = $-$g (Ball is thrown upward)

Using the third equation of motion, $v^2=u^2-2g{h}_{\max }$

$$\begin{gathered} \Rightarrow 0=u^2-2\times 10\times 5 \\ \Rightarrow u^2=100 \\ \Rightarrow u=10\mathrm{m}/\mathrm{s} \end{gathered}$$

Hence, the initial velocity of the ball is 10 m/s.

(ii) To calculate the time taken by the ball to reach the maximum height, we would use the first equation of motion.

$$\begin{gathered} v=u-gt \\ \Rightarrow 0=10-10t \\ \Rightarrow t=1\mathrm{s} \end{gathered}$$

Hence, the time taken by the ball to reach the maximum height is 1 second.