Question

A ball is thrown up and attains a maximum height of $19.6m$. Its initial speed was :

• A. $9.8m{s}^{-1}$
• B. $44.3m{s}^{-1}$
• C. $19.6m{s}^{-1}$
• D. $98m{s}^{-1}$

Answer 1

The correct option is C

$19.6m{s}^{-1}$

Step 1: Given

Height, $h=19.6m$

Acceleration due to gravity$g=9.8m/s^2$

(AS ball thrown up that's why the negative sign is taken)

Final velocity$=0$

initial velocity$=u$

Step 2: Calculating initial velocity

Using third equation of motion

$$\begin{gathered} {\mathit{v}}^{\mathbf{2}}\mathbf{=}{\mathit{u}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathit{g}\mathit{h} \\ {\mathbf{\left(}\mathbf{0}\mathbf{\right)}}^{\mathbf{2}}\mathbf{=}\mathit{u}\mathbf{+}\mathbf{2}\mathbf{(}\mathbf{-}\mathbf{9}\mathbf{.}\mathbf{8}\mathbf{)}\mathbf{\times }\mathbf{19}\mathbf{.}\mathbf{6} \\ {\mathit{u}}^{\mathbf{2}}\mathbf{=}\mathbf{19}\mathbf{.}\mathbf{6}\mathbf{\times }\mathbf{19}\mathbf{.}\mathbf{6} \\ \mathit{u}\mathbf{=}\mathbf{19}\mathbf{.}\mathbf{6}\mathit{m}\mathbf{/}\mathit{s} \end{gathered}$$

Hence, the initial velocity is $19.6m/s$.

The Correct option is (C).