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6 June, 11:22

A flower pot falls from a balcony of an apartment building in Salem, Oregon and injures a person. Your job is to determine the apartment from which it originated. Video footage from the second floor indicates that it traveled past a 4.000 meter high window in 0.2600 seconds. All floors in the building are 4.000 meters high. From which floor was the flower pot dropped

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  1. 6 June, 11:49
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    The pot was dropped from the fourth floor.

    Explanation:

    The height and velocity of the pot is given by the following equations:

    y = y0 + v0 · t + 1/2 · g · t²

    v = v0 + g · t

    Where:

    y = height at time "t".

    y0 = initial height.

    v0 = initial velocity.

    t = time.

    g = acceleration due to gravity.

    v = velocity at time "t".

    Let's place the origin of the frame of reference on the ground. We know that from the second floor (y = 8.000 m) the pot traveled 4.000 m in 0.2600 s. Then:

    y = y0 + v0 · t + 1/2 · g · t²

    4.000 m = 8.000 m + v0 · 0.2600 s - 1/2 · 9.8 m/s² · (0.2600 s) ²

    (4.000 m + 1/2 · 9.8 m/s² · (0.2600 s) ² - 8.000 m) / 0.2600 s = v0

    v0 = - 14.11 m/s

    This velocity is the velocity of the pot when it is at a height of 8.000 m (on the second floor).

    Now let's find how much time it took the pot to reach that velocity starting from rest (the pot was dropped, not thrown. Then v0 = 0).

    v = v0 + g · t

    -14.11 m/s = 0 - 9.8 m/s² · t

    t = - 14.11 m/s / - 9.8 m/s²

    t = 1.440 s.

    This is the time it takes the pot to reach the second floor (y = 8.000 m). So, let's calculate y0 using the equation of height:

    y = y0 + v0 · t + 1/2 · g · t² (v0 = 0)

    8.000 m = y0 - 1/2 · 9.8 m/s² · (1.440 s) ²

    8.000 + 1/2 · 9.8 m/s² · (1.440 s) ² = y0

    y0 = 18.16 m

    The pot was dropped from (18.16 m / 4 = 4.54) the fourth floor.
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