Question

a) 450 m
b) 900 m
c) 1800 m
d) 2000 m

Please please explain this well to me...please give a proper explanation
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Answer 1

Answer:

distance = speed × time

1500*1.2

=1800.0

Answer 2

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$\huge{ \underline{ \rm{ \green{Answer....}}}}$

♦️ GiveN:

• A pulse of sound is created from boat which gets reflected after hitting the bottom of sea.
• Total time of sound reaching again = 1.2 s
• Speed of the sound = 1500 m/s

♦️To FinD:

• Distance between the boat and the bottom of sea bed.....?

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$\huge{ \underline{ \rm{ \green{Explanation....}}}}$

This question can be solved by using simple average speed, distance, time formula or by using direct formula (i.e. the derived formula only). The question is based on SONAR concept of sounds, which is the reflection of sound by hitting the sea beds. It has wide applications like used in submarines especially.

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⸙ Formula for Average speed:

$\large{ \ast{ \boxed{ \rm{ \red{Avg. \: speed = \frac{total \: distance}{total \: time \: taken}}}}}}$

Here, in this question, the speed of sound is only the average speed of sound. From this we can calculate distance as total time is also given.

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⸙ Formula for sonar or echo ranging:

$\large{ \ast{ \boxed{ \rm{ \red{Distance\: b/w \:boat \:and \:bottom\:= \frac{v \times t}{t}}}}}}$

♠️ Note:

This is formula is derived from avg. speed formula only.

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Now, solving this question by using both formulas.

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$\huge{ \underline{ \rm{ \green{Solution...}}}}$

♦️ Refer to the attachment....

$\large{ \boxed{ \purple{ \rm{Using \: formula - 1}}}}$

Let the distance between the boat and bottom of sea bed be d, then total distance = 2d

Total time taken = 1.2 s

Avg. speed = 1500 m/s

By using avg. speed formula,

$\large{ \rm{ \rightarrow \: 1500 = \frac{total \: distance}{1.2 \: s}}} \\ \\ \large{ \rm{ \rightarrow \: total \: distance \: = 1500 m {s}^{ - 1} \times 1.2 s}} \\ \\ \large{ \rm{ \rightarrow \: total \: distance = \frac{1500 \times 12}{10}m}} \\ \\ \large{ \rm{ \rightarrow \: total \: distance = 1800 \: m}}$

We have total distance = 2d

Then, d = 1800 / 2 m = 900 m

$\large{ \rm{ \therefore{ \underline{ \pink{Distance \: b/w \: boat \: and \: sea \: bed = 900 \: m}}}}}$

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$\large{ \boxed{ \rm{ \purple{ Using \: formula - 2}}}}$

We have, v = 1500 m/s

total time t = 1.2 s

Then, by using this direct formula,

$\large{ \rm{ \rightarrow \: d = \cancel{\frac{1500 \times 1.2}{2} m}}} \\ \\ \large{ \rm{ \rightarrow \: d = 900 \: m}}$

$\large{ \rm{ \therefore{ \underline{ \pink{Distance \: b/w \: boat \: and \: sea \: bed = 900 \: m}}}}}$

$\large{\ast\: \:{\underline{\rm{\blue{Option \: B}}}}}$

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