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A ball is dropped from the top of a 55.0 m high cliff

  1. Jun 1, 2017 #1
    1. The problem statement, all variables and given/known data
    A ball is dropped from the top of a 55.0 m -high cliff. At the same time, a carefully aimed stone is thrown straight up from the bottom of the cliff with a speed of 21.0 m/s . The stone and ball collide part way up.

    How far above the base of the cliff does this happen?
    2. Relevant equations
    d = vt+1/2at^2
    d1 + d2 = 55

    3. The attempt at a solution
    Ball

    v = 0
    d = 1/2*9.8t^2

    Stone
    v = 21
    d = 21t-1/2*9.8t^2 (I made it -9.8 because the stone is going up so it's fighting gravity, I hope I'm right)

    Ball + Stone = 55
    1/2*9.8t^2 + 21t-1/2*9.8t^2 = 55
    21t = 55
    t = 2.619

    Stone:
    21(2.619)-(1/2)(9.8)(2.619)^2 = 21.389

    Ball:
    (1/2)(9.8)(2.619)^2 = 33.6109

    I don't understand what I'm supposed to do next.
     
  2. jcsd
  3. Jun 1, 2017 #2

    PeroK

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    What do you mean next? You've got the answer, surely?

    Note that you need to add units to your working, e.g. ##t = 2.619s##.

    An an aside: the stone starts off at ##21m/s## and the initial distance between the stone and the ball is ##55m##. What do you get if you divide ##55## by ##21##?
     
  4. Jun 1, 2017 #3

    ehild

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    Stone:
    21(2.619)-(1/2)(9.8)(2.619)^2 = 21.389

    Ball:
    (1/2)(9.8)(2.619)^2 = 33.6109

    I don't understand what I'm supposed to do next.[/QUOTE]
    You have to answer the question: How far above the base of the cliff does this happen?
    You got two numbers, explain what they mean. First, add units, as @PeroK said.
    Clarify, at what distance from the base of the cliff the ball and stone collide.
     
  5. Jun 1, 2017 #4
    When I divided 55/21, I got 2.619 (the same number as I got for seconds). I got 2 answers, the displacement for the ball (33.6109m) and the displacement for the stone (21.389m).
     
  6. Jun 1, 2017 #5

    PeroK

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    How far about the cliff is the collision? Hint: think about the stone.

    Is ##55/21 = 2.619## a coincidence?
     
  7. Jun 1, 2017 #6

    ehild

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    Answer the question: How far above the base of the cliff does the collision happen?
     
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