Question

To estimate the height of a bridge over a river, a stone is dropped freely on the river from the bridge. The stone takes \[2{\text{ s}}\] to touch the water surface of the river.Calculate the height of the bridge from the water level .Take \[{\text{g}} = 9.8\,m/{s^2}\] .
A. \[19.6\,m\]
B. \[9.8\,m\]
C. \[21.4\,m\]
D. \[4.9\,m\]

Answer 1

Hint:In Newton Physics, the free fall occurs when a motion takes place on a body and there will be only one force acting upon it that is gravity. Now the equations of motions are derived from the usual equations by substituting initial velocity \[u = 0\] .Then using equations of motion we find the value of the height of the bridge over a river.

Complete step by step answer:
The free fall motion has the effect of acceleration because of gravity. Let's take an object which is freely falling for t seconds from height h, due to gravity g. Now the equations of motions are as follows;
\[(i)h = \dfrac{1}{2}g{t^2}\]
\[(ii){v^2} = 2gh\]
\[(iii)v = gt\]
Time taken by the stone to touch the surface of water was given as \[t = 2\,s\].
\[h = ?\]
We need to find the height of the bridge which is actually the height from which the stone was dropped, now this is the total displacement of the stone. The total displacement of stone which is height of bridge can be computed using the equation of motion
\[h = \dfrac{1}{2}g{t^2}\]
\[ \Rightarrow h = \dfrac{1}{2} \times 9.8{\left( 2 \right)^2}\]
\[ \therefore h = 19.6\,m\]

Therefore, the correct answer is option \[{\text{A}}\].

Note:Sometimes students forget to consider the initial velocity of the object during free fall as zero. So here initial velocity won’t affect but that might mislead the concept.When an object is dropped from a height, it moves under the sole influence of gravitational force due to earth.