Question

To estimate the height of a bridge over a river, a stone is dropped from the bridge. It takes $3seconds$to touch the surface of water. Calculate the height of the bridge. [ Take $g=9.8m{s}^{-2}$]

Answer 1

Step 1: Given data

Initial velocity of stone, $u=0$

Time taken, $t=3s$

Acceleration due to gravity, $g=9.8m{s}^{-2}$

Height, $h=?$ (To be calculated)

Step 2: Calculating the height of the bridge

Applying equation of motion for the freely falling object,

$$\begin{gathered} h=ut+\frac{1}{2}g{t}^2 \\ \Rightarrow h=0\times 3s+\frac{1}{2}\times 9.8m{s}^{-2}\times {(3s)}^2 \\ \Rightarrow h=44.1m \end{gathered}$$ [ '$g$' is positive when a body falls downwards]

Hence, the height of the bridge is $44.1m$