Question

Sardar Baji Prabhu Deshpande fighting at the Ghodkhind pass 480 m from the Panhalgad was waiting to hear the cannon boom from Vishalgad 240 m away on the opposite side. He saw the flash of the cannon 0.8 sec before he heard the boom. He dropped his sword from a height of 5 m as soon as he heard the boom. x milliseconds after his sword fell on the ground, he heard the sound of the cannon again. What is the value of x? (g = 10)

Answer 1

The value of x is 600 milliseconds

Step-by-step explanation:

Distance of Vishalgarh from Sardar Baji Prabhu Deshpande = 240 m

We know that speed of light $=3\times 10^8$ m/s

Therefore, the time taken bu the flash of boom to reach the Sarda

$=\frac{240}{3\times 10^8}$

$=8\times 10^{-7}$ seconds

He heard the sound of cannon boom after 0.8 seconds

Therefore,

Time taken by the Sardar to hear the sound

$=0.8+8\times 10^{-7}$

$=0.8$ seconds  (approx.)

Speed of sound

$=\frac{240}{0.8}$ m/s

$=300$ m/s

At this time he drops his sword from 5 m height

Time taken by the sword to reach the ground

Using second equation of motion

$h=ut+\frac{1}{2}gt^2$

$5=0\times t+\frac{1}{2}\times 10 t^2$

$\implies 5=5t^2$

$\implies t=1$ second

$\impliesm t=1000$ millisecond

The sardar hers the sound of echo coming from 480 m away Panhalgad after (1000 +  x) millisecond

Thus,

Distance = Speed of sound x time

$480=300\times (1000+x)\times 10^{-3}$

$\implies 1000+x=\frac{480\times10^3}{300}$

$\implies 1000+x=1600$

$\implies x=1600-1000$

$\implies x=600$ milliseconds

Hope this answer is helpful.

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