Question

A sound wave sent from a stationary submarine returns 10 seconds later after hitting an underground object. Another signal sent after 5 seconds returns in 8 seconds. If the speed of signal in water is 1500 m/s, then calculate the speed at which the underground object is moving towards the submarine.​

Answer 1

Answer:

A sonar device on a submarine sends out a signal and receives an echo 5 s later. Calculate the speed of sound in water if the distance of the object from the submarine is 3625 m.

Explanation:

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Answer 2

The negative value of v doesn't make physical sense in this context, so we reject it. Therefore, the speed at which the underground object is moving towards the submarine is approximately 600 m/s.

Let's call the distance from the submarine to the underground object "d", and let's call the speed at which the object is moving towards the submarine "v". We can use the formula:

distance = speed × time

To solve for "d" and "v".

For the first signal:

distance = 2d (since it goes to the object and comes back)

$time = 10 seconds\\speed = 1500 m/s$

Therefore:

$2d = 1500 \times 10\\2d = 15000\\d = 7500 meters$

For the second signal:

distance = d

$time = 8 - 5 = 3 seconds$

$speed = 1500 m/s$

Therefore:

$d = 1500 \times 3\\d = 4500 meters$

Now we can set up an equation for the speed of the object:

$d1 = (v + 1500) \times 10\\d2 = (v + 1500) \times 5$

where d1 is the distance traveled by the first signal and d2 is the distance traveled by the second signal.

Substituting the values we calculated, we get:

$7500 = (v + 1500) \times 10\\4500 = (v + 1500) \times 5$

Simplifying each equation, we get:

$7500 = 10v + 15000\\4500 = 5v + 7500$

Solving for v in each equation, we get:

$v = -750 m/s\\v = 600 m/s$

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