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Little Milly/Willy/Time and Height

  1. Dec 7, 2009 #1
    1. The problem statement, all variables and given/known data

    Little Willy, clumsy clot,
    From window sill dislodged a pot.
    He shouts below to Little Milly:
    "Step aside, it'll knock you silly!"


    The window sill is 35.0 m above the sidewalk where Millly is standing directly below the falling pot. Milly is 1.05 m tall, her ears are 5.00 cm below the top of her head, and she needs 0.400 s to respond to the warning. The speed of sound in air is 340 m/s. What is the minimum height of the pot above the ground at the instant Willy shots his warning if Milly is to avoid being "potted"? Answer in m.

    2. Relevant equations

    v =d/t
    d = (v1)t + 0.5a(t^2)

    3. The attempt at a solution

    So I first found the time is takes for the sound to reach Milly's ears:

    t = d/v
    t = (35.0m - 1.0m)/(340m/s)
    t = 0.10 s

    So the time it takes Milly to receive the warning and respond:

    0.10 s + 0.400 s = 0.50 s

    I use d = (v1)t + 0.5a(t^2) to find the distance the pot falls:

    d = (v1)t + 0.5a(t^2) ...where v1 is 0
    d = 0.5(-9.8)(0.50)^2
    d = 1.225 m

    I'm not sure what to do next or if I even started this question correctly. All input is appreciated!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 7, 2009 #2
    Alright, scratch the top part. I've thought of this as a solution and was wondering if anyone can confirm this.

    i. Time is takes for the sound to reach Milly:

    t = d/v = (35.0 m - 1.0 m)/340 m/s = 0.10s

    ii. Time is takes for warning to reach Milly and for her to respond:

    0.10 s + 0.400 s = 0.50 s

    iii. Time it takes the pot to hit Milly's head:

    d = 33.95 m; v1 = 0; a = 9.80 m/s2

    d = v1t + 0.5at2
    33.95 = (0.5)(9.80)t2
    t = 2.63 s

    Time Willy needs to warn Milly:

    2.63 s - 0.50 s = 2.13s

    Distance the pot will fall:

    t = 2.13 m; v1 = 0; a = 9.80 m/s2

    d = v1t + 0.5at2
    d = 0.5(9.80)(2.13)2
    d = 22.28 m

    Height of the pot above the ground:

    35.0 m - 22.28 m = 12.7 m
     
  4. Dec 7, 2009 #3
    looks good.
     
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