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A construction worker on the 24th floor of a building project accidentally drops a wrench and yells “Look out below” Could a person of ground level hear his warning in time to get out of the way? The speed of sound is about 1100 feet per second

User Gift
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Answer:

Assuming the height at which the wrench was dropped is 336 feet,

the person will hear the sound in 0.3 sec and the wrench will hit the ground only after 4.58 seconds so there is enough time to get out of the way

Step-by-step explanation:

Without knowing the exact height at which the 24th floor is located, it would be difficult to determine whether the wrench will hit the ground before the sound hits the ground

Realistically, we can assume each floor of the building is 14' high

So the height at which the 24th floor is located is 24 x 14 = 336 feet

To travel 336 feet at 1100 feet per second, sound will take 336/1100 seconds which is 0.30 second

Let's compute the time taken for the wrench to hit the ground

The acceleration due to gravity is usually taken to be 16 feet/second²

The displacement which is the distance traveled by an object with an initial velocity of u in time t is given by the equation:
s = ut + (1/2)t²

Here the initial velocity is 0

So the equation is
s = 1/2 x 32 x t² = 16t²

To cover 336 feet we substitute 336 for s and get

336 = 16t²

t² = 336/16

t = ±√(336/16) ≈ 4.58 seconds (we only take the positive root)

So the person will hear the sound in 0.3 sec and the wrench will hit the ground only after 4.58 seconds so there is enough time to get out of the way

In general, we can state that if the height from which the wrench was dropped is h then time t taken for wrench too hit the ground is

t = √(h/16) seconds

If this is greater than the time taken for sound to travel the same distance then the person can get out of the way

User Ron Maupin
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