Question

A thunder is heard 5 seconds after the lightning flash. The distance of the flash is (velocity of sound in air is $345\,m/s$ ):
A. $3560\,m$
B. $1725\,m$
C. $1780\,m$
D. $1825\,m$

Answer 1

We know that velocity is the ratio of displacement to the time taken. From this we can calculate the value of displacement since both value of velocity of sound in air and time taken is given. That will give us the distance travelled by the flash.

Complete step by step answer:
It is given that a thunder tap is heard 5 seconds after the lightning flash.
The velocity of sound in air is given as $345\,m/s$.
We need to calculate the distance travelled by the flash.
In this case, the distance travelled by the light and the thunder sound is the same.
But light reaches us first due to its high speed compared to sound.
We know that velocity is given as the ratio of displacement to the time taken.
In equation form, we can write velocity as
$v = \dfrac{d}{t}$
Where $d$ is the displacement or the shortest distance between the initial and final positions and $t$ is the time taken.
From this equation, we can calculate the displacement as a product of velocity and time.
$\Rightarrow d = v \times t$ ………………..(1)
Since it is given that the thunder is heard after 5 seconds, we get the time $t = 5\,s$.
Velocity of sound in air, $v = 345\,m/s$ .
Substituting these values in equation (1), we get
$\Rightarrow d\, = 345 \times 5\,m$
$\Rightarrow d = 1725\,m$

$\therefore$ The distance travelled by the flash. So, the answer is option (B).

Note:
Remember that the displacement is the shortest distance between the initial and final positions. Distance is the total length of the path travelled. The ratio of distance to time will give us the speed which is a scalar quantity. The ratio of displacement to time gives us the velocity. Whenever a particle is travelling in a straight line in that case both the displacement and distance will be equal. So, in our case, the distance of the flash is the same as the displacement.