Question

A stone is dropped freely from the top of a tower and it reaches the ground in 4 sec taking (g = $10m{{s}^{-2}}$). Calculate the height of the Tower.
a.) 20m
b.) 40m
c.) 60m
d.) 80m

Answer 1

Hint: We have to assume the initial speed as zero and the duration of time is given in the question. So we can apply the equation of motion in this equation. There are three equations of motion and we have to find the suitable one for it. We have to find the height of the tower when initial velocity is zero given with time 4 seconds. Hence, we will use $s=ut+\dfrac{1}{2}a{{t}^{2}}$

Formula Used:
$s=ut+\dfrac{1}{2}a{{t}^{2}}$

Complete Step by Step Solution:
We have given the time (t) as 4 seconds.

And let us assume that the initial velocity is zero and the height of the tower is (s). where a will be the acceleration due to gravity which is given as (g = $10m{{s}^{-2}}$).

Now put all these equations in the formula
$s=ut+\dfrac{1}{2}a{{t}^{2}}$
Where (s) is the height of the tower and (t) is the time and (a) is the acceleration due to gravity and (u) is the initial speed.

Putting the given values in the above equation we get.
\[s=0+\dfrac{1}{2}(10){{(4)}^{2}}\]
$s=0+10\times 8$
$s=80m$

Since we have assumed that (s) is the height of the tower and we got $s=80m$ from the above equation

Hence our solution for the question is that the height of the tower is 80 meters.
We can conclude that option (d) is the correct answer.

Note:
When we are given with an initial velocity(u) with a time(t) and we are asked about the distance then the only formula that satisfies our need is $s=ut+\dfrac{1}{2}a{{t}^{2}}$ because in this formula we are given with three quantities and has been asked for the fourth one. In other equations of motion we do not have the combination for these three given quantities.