(b) A person drops a stone into a well 180 m deep. After how much time, from the instant he drops the stone, will the sound of splash of water be heard by the person? (g = 10 m/s² ; speed of sound in air -330 m/s).
pls solve quickly and correctly
pls solve quickly and correctly
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Answer:
To find the time it takes for the sound of the splash to reach the person, we need to consider two things: the time it takes for the stone to fall and the time it takes for the sound to travel back up.
First, let's calculate the time it takes for the stone to fall. We can use the equation of motion:
h = (1/2)gt^2
where h is the height (180 m) and g is the acceleration due to gravity (10 m/s²).
180 = (1/2)(10)t^2
Simplifying the equation, we get:
t^2 = 36
Taking the square root of both sides, we find:
t = 6 seconds
So, it takes 6 seconds for the stone to fall to the bottom of the well.
Now, let's calculate the time it takes for the sound to travel back up. We can use the equation:
distance = speed × time
The distance is twice the depth of the well (360 m) because the sound needs to travel down and back up. The speed of sound in air is given as 330 m/s.
360 = 330 × time
Simplifying the equation, we get:
time = 360 / 330
time ≈ 1.09 seconds
Therefore, it takes approximately 1.09 seconds for the sound of the splash to reach the person's ears after they drop the stone into the well.
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