Question

A stone is released from the top of tower $19.6m$ high. If $g=9.8m{s}^{-2}$, the final velocity of the stone on reaching the ground is:

• A. $9.8m{s}^{-2}$
• B. $28.4m{s}^{-2}$
• C. $19.6m{s}^{-2}$
• D. none of the above

Answer 1

The correct option is C

$19.6m{s}^{-2}$

Step 1: Given

The initial velocity of stone, $u=0m{s}^{-1}$

Acceleration due to gravity, $g=9.8m{s}^{-2}$

The final velocity of the stone, $v=?$ (To be calculated)

Height of the tower, $h=19.6m$

Step 2: Calculating the final velocity of the stone

Applying the equation of motion for the freely falling object,

$$\begin{gathered} v^2=u^2+2gh \\ \Rightarrow v^2=0+2\times 9.8m{s}^{-2}\times 19.6m \\ ⟹v=19.6m{s}^{-1} \end{gathered}$$

( '$g$' is positive when a body falls downwards)

Therefore, the final velocity of the stone on reaching the ground is $19.6m{s}^{-1}$

Hence, the correct answer is option (C) i.e. $19.6m{s}^{-1}$