a pabble is dropped from the top of the building on a glass at the ground, the sound of splash is heard after 5 second. if the velocity of sound is 330 m/ sec. find the height of the top of the building
height = 5(330) m
= 1650 m !!!!!
Exactly where are you on earth?
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To find the height of the top of the building, we need to consider the time it takes for the splash sound to reach the ground.
The total time taken can be calculated by adding the time it takes for the pebble to fall and the time it takes for the sound to travel back up to the top of the building.
Since the pebble is dropped, we can use the equation for free fall:
d = (1/2)gt^2
where:
d = distance
g = acceleration due to gravity (9.8 m/s^2)
t = time
In this case, the distance is equal to the height of the building, and the time is the falling time. Let's call this "t1".
So, we have:
height = (1/2) * 9.8 * t1^2
Next, we know that the sound travels with a velocity of 330 m/s. Thus, the time it takes for the sound to travel from the ground back up to the top of the building is equal to the time it takes for the pebble to fall. Let's call this "t2".
height = 330 * t2
Since the total time taken is 5 seconds, we can express it as:
t1 + t2 = 5
Now, we have two equations with two unknowns. We can solve for "t1" and "t2" using substitution or elimination. Let's solve it using substitution.
From the second equation, we can express t2 in terms of the height:
t2 = height / 330
Substituting this expression into the first equation:
height = (1/2) * 9.8 * (height / 330)^2
Simplifying the equation, we get:
1 = (1/2) * 9.8 * (height / 330)^2
Rearranging, we have:
(height / 330)^2 = 2 / 9.8
Taking the square root of both sides:
height / 330 = sqrt(2 / 9.8)
Now, let's solve for the height:
height = 330 * sqrt(2 / 9.8)
Using a calculator, we can find the approximate value of the above expression:
height ≈ 29.19 meters
Therefore, the height of the top of the building is approximately 29.19 meters.