How high is the building?

A physics student with too much free time drops a watermelon from a roof of a building, hears the sound of the watermelon going "splat" 2.5s later. How high is the building? The speed of sound is 340m/s. You may ignore air resistance.

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  • 7 years ago
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    The formula the distance of a free falling object is

    s = 0.5 * g * t1² (1)

    The formula for the distance sound travels is

    S = Velocity * t2 (2)

    The total time for the mellon to fall and the sound return is T =t1 + t2. T = 2,5

    2.5 = t1 + t2 (3)

    Equating the formulas for the distance

    (0.5 * g * t1²) = 340 * t2 (sound velocity is 340 m/s)

    4.9 * t1² = 340 * t2

    t2 = (4.9 * t1²) / 340

    Substituting the value of t2 into formula (3)

    2.5 = t1 + ((4.9 * t1²) / 340)

    850 = 340t1 + 4.9t1²

    4.9t1² + 340t1 - 850 = 0

    using an online quadratic formula calaulator, the roots for t1 are

    2.415885683 and -71.8.....

    Using the real root, t2 is 2.5 - 2.415885683 = 0.084114317 seconds

    This makes the building 0.084114317 * 340 = 28.5988678 n tall

    Checking with formula (1)

    S = 0.5 * g * t1²

    S = 4.9 * 2.415885683²

    S = 4.9 * 5.83650.....

    S = 28.5988678....

    The 2 calculations are the same, so this is your answer.

    TexMav

  • 7 years ago

    I'm choosing a method that

    evades the quadratic formula.

    If the sound were transmitted instantaneously,

    the 2.5s would be the time for the melon to fall,

    and you'd have h = (1/2)gt^2

    = (1/2)(4.9 m/s^2)(2.5 s)^2 = 30.625 m,

    and the time for the sound to rise 30.6 m

    would be only 0.090 seconds.

    So back up and assume the time

    for the melon to fall was 2.410 s; then

    h = (1/2)gt^2 = 28.46 m, and the time

    for the sound to rise is 0.084 s.

    If the time to fall were 2.416 s, then

    h = (1/2)gt^2 = 28.60 m, and the time

    for the sound to rise is 0.08412 seconds.

    If the time to fall were 2.41588 s, then

    h = 28.5987 m, etc.

    Concluding that h = 28.60 meters.

  • 7 years ago

    Let the height of the building be h

    Time to fall = √(2.h/g)

    Time for sound of impact to return to student = h/340

    Therefore: √(2.h/g)+h/340 = 2.5 which (with g=9.8) solves to give h = 28.6 m

  • 7 years ago

    Speed=distance/time

    Therefore--> distance=speed x time

    So... speed=340m/s and time=2.5s

    Dist= 340 x 2.5 = 850m

    If in doubt use your units. Speed in m/s basically means metres divided by seconds, hence your speed is distance divided by time.

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  • Anonymous
    7 years ago

    First,air resistance does not matter in propagation of sound..

    Second,data inadequate....

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