Question

A body is dropped from a height $H$ . What is the time taken to cover the second half of the journey?

Answer 1

In order to answer this question, first we will assume the time takes as $'T'$ i.e.. the whole time taken of the dropping of the body and we will find the value of it. And again we will assume the time taken as $'t'$ i.e.. first half of the journey. Now, we can take the difference between two time values to get the value of time taken to cover the second half of the journey.

Complete step by step answer:
Let the body take time $'T'$ to reach the ground. Then, now we will apply the formula of height in terms of gravity and time:-
$H = 0.5g{t^2}$
And, $T = \sqrt {\dfrac{{2H}}{g}}$
where, $g$ is the gravity.
Again, if it takes time $'t'$ to travel first half of the journey then,
$0.5H = 0.5g{t^2}$
And, $H = g{t^2}$
$\Rightarrow t = \sqrt {\dfrac{H}{g}}$
Now, timer taken to cover second half of the journey, is: $T - t$
So, we will substitute both the above values of $T\,and\,t$ :
$\sqrt {\dfrac{{2H}}{g}} - \sqrt {\dfrac{H}{g}} = \sqrt {\dfrac{H}{g}} \times (\sqrt 2 - 1)$

Hence, the required time taken to cover the second half of the journey is $\sqrt {\dfrac{H}{g}} \times (\sqrt 2 - 1)$.

Note: The object will be influenced by only one force, namely gravity. The object is dragged towards the earth's centre by the earth's gravitational force. Its velocity steadily increases under this force until it reaches the earth.