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 velocity with which it hits the surface of water. [ 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, $g=9.8m{s}^{-2}$

Final velocity of the stone, $v=?$ (To be calculated)

Step 2: Calculating the final velocity of the stone

Applying equation of motion for the freely falling object,

$$\begin{gathered} v=u+gt \\ \Rightarrow v=0+9.8m{s}^{-2}\times 3s \\ \Rightarrow v=29.4m{s}^{-1} \end{gathered}$$ [ '$g$' is positive when a body falls downwards]

Hence, the final velocity of the stone is $29.4m{s}^{-1}$.