Question

A stone is dropped from a certain height which can reach the ground in \[5{\text{ }}s\] . If the stone is stopped after \[3{\text{ }}s\] of its fall and then allowed to fall again, then the time taken by the stone to reach the ground for the remaining distance is:
A.$2\,s$
B.$3\,s$
C. $4\,s$
D. $8\,s$

Answer 1

Hint:In order to answer this question, to know about the time taken by the stone to reach the ground for the remaining distance we will use the formula from elementary physics .We will do it in two parts first one is for the distance covered in \[3{\text{ }}s\] and then finally the remaining distance covered in how many seconds.

Formula used:
$h = \dfrac{1}{2}g{t^2}$
With a starting velocity of zero, the \[\left( h \right)\] is the distance a projectile has travelled after time \[\left( t \right)\] . The acceleration due to gravity constant \[\left( g \right)\] has a value of \[9.8\] metres per second squared \[\left( {9.8m/{s^2}} \right)\]

Complete step by step answer:
Freefall is a physics term that describes a condition in which the only force acting on an item is gravity, resulting in acceleration owing to gravity. The phrase "freefall" refers to a body falling freely due to the earth's gravitational force. Gravitational acceleration will occur as a result of this motion. The three equations of motion under gravity will govern this form of motion.

Now, coming to the question;
Let, $h$ be the height, $t$ = $5s$
$h = \dfrac{1}{2}g{t^2} \\
\Rightarrow h = \dfrac{1}{2}\left( {9.8} \right)\left( {25} \right) \\
\Rightarrow h = 122.5\,m$
$\text{Distance covered in}\, 3{\text{ }}s= \dfrac{1}{2}\left( {9.8} \right){\left( 3 \right)^2} \\
\Rightarrow \text{Distance covered in}\, 3{\text{ }}s= \dfrac{1}{2}\left( {9.8} \right)\left( 9 \right) \\
\Rightarrow \text{Distance covered in}\, 3{\text{ }}s= 44.1\,m$
Remaining distance = $122.5 - 44.1 = 78.4\,m$
If $t\,$sec is the required time, then
$78.4 = 0 + \dfrac{1}{2}g{t^2} \\
\Rightarrow {t^2} = \dfrac{{784}}{{49}} = 16 \\
\therefore t = 4\,s $
Therefore the remaining distance is covered in $4\,s$.

So, the correct option is C.

Note: Another important category of free-fall problems is projectile motion.Although these processes take place in three dimensions, they are treated as two-dimensional on paper for the sake of basic physics.