Question

A stone dropped from the top of a tower of height 300 m high splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is $340m{{s}^{-1}}$.

Answer 1

Hint: Find the time taken by the stone to travel the distance of 300m till it splashes into the water near the base of the tower. Next, as speed of sound is given, we can calculate the time taken by sound to travel the same 300m. If we add both the time taken, we will get the sound.

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

Complete step by step answer:
Let us first find the time taken by the stone to reach the bottom of the tower.
As distance, and initial velocity is given, acceleration is the acceleration due to gravity, we get time as,
$\begin{align}
  & 300=(0)t+\dfrac{1}{2}(9.8){{t}^{2}} \\
 & \Rightarrow t=7.82s \\
\end{align}$
Now, let us find the time taken by the sound to travel the same distance, i.e. 300m
$\begin{align}
  & t=\dfrac{s}{v} \\
 & \Rightarrow t=\dfrac{300}{340}s \\
 & \Rightarrow t=0.88s \\
\end{align}$
Therefore, the total time taken by the sound to reach the top of the tower will be,
$\begin{align}
  & t=7.82+0.88s \\
 & \Rightarrow t=8.7s \\
\end{align}$
Therefore, waves obtain the total time taken by the sound to reach the given distance.

Additional Information: In some situations, where the acceleration of the given body is constant, the above used equations involving initial velocity, final velocity, acceleration and the time can be used to find out the unknown quantity.
Newton's laws of motion are three physical laws that laid the foundation for classical mechanics together. They describe the relation between a body and the forces acting upon it and its motion in response to external forces. The first law defines the force qualitatively. The second one offers a quantitative measure of force. Third law explains about a single isolated force that does not exist.

Note: In the above question, the acceleration of the stone is equal to the acceleration of gravity. Clearly, the acceleration is constant. Therefore, this equation can be used to find out the unknown term, that is the time taken. Also, the object is freely falling which tells that the initial velocity is equal to zero.