Question

A stone is dropped from a cliff. Find its speed after the stone has fallen from 100 m. (Take $g=9.8m{s}^{-2}$).

• A. $9.8m{s}^{-1}$
• B. $19.6m{s}^{-1}$
• C. $44.2m{s}^{-1}$
• D. $24m{s}^{-1}$

Answer 1

The correct option is C

$44.2m{s}^{-1}$

In case of free fall, the body would accelerate with 'g' (Therefore, a = g)
Given, initial velocity, u =$0m{s}^{-1}$ (initially stone is at rest), acceleration due to gravity, g = $9.8m{s}^{-2}$ and height, h = 100 m.
Let the final velocity be 'v'.
In the case of free fall, the third equation of motion becomes , $v^2$​ = $u^2$​ + 2gh
$v^2$​​ =​ 0 + 2 $\times$ 9.8 $\times$ 100
$\Rightarrow$$v^2$​​ = 1960
$\Rightarrow$v = $\sqrt{1960}$ = 44.2 $m{s}^{-1}$