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Math Help - "A ball is thrown up from the rooftop"

  1. #1
    s3a
    s3a is offline
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    "A ball is thrown up from the rooftop"

    "A ball is thrown up from the rooftop with an initial speed of m/s. 1.84 s later, another ball is dropped from the rooftop.

    a) Assuming that neither has landed, where and when do they meet?
    m from the rooftop
    at seconds from the moment the first ball was thrown.

    b) What are their speeds when they meet?
    The first ball : m/s
    The second ball : m/s"

    All my answers are wrong, except t = 2.065. I would appreciate it a lot if someone could help me do this question!

    Thanks in advance!
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  2. #2
    MHF Contributor
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    Hello s3a
    Quote Originally Posted by s3a View Post
    "A ball is thrown up from the rooftop with an initial speed of m/s. 1.84 s later, another ball is dropped from the rooftop.

    a) Assuming that neither has landed, where and when do they meet?
    m from the rooftop
    at seconds from the moment the first ball was thrown.

    b) What are their speeds when they meet?
    The first ball : m/s
    The second ball : m/s"

    All my answers are wrong, except t = 2.065. I would appreciate it a lot if someone could help me do this question!

    Thanks in advance!
    Using the equation
    s=ut+\tfrac12at^2
    and taking t = 0 when the first ball is thrown, the height h_1 of the first ball above the roof at time t seconds is given by:
    h_1=10t-4.9t^2, taking g = 9.8
    The height h_2 of the second ball above the roof at time t is:
    h_2 = -4.9(t-1.84)^2
    They meet when h_1= h_2; i.e. when:
    10t-4.9t^2=-4.9(t-1.84)^2
    =-4.9t^2+18.032t-16.58944
    \Rightarrow 8.032t = 16.58944

    \Rightarrow t = 2.0654
    So, as you say, they meet after 2.0654 seconds.

    When t = 2.0654,
    h_2 = -4.9(2.065-1.84)^2=-0.249
    So the meet 0.249 m below the level of the roof.

    Using v = u+at, the speed of the first ball is:
    10-9.8\times2.0654=-10.24
    i.e. 10.24 m/sec.

    And the speed of the second = 0-9.8\times(2.0654-1.84) =-2.209

    i.e. 2.209 m/sec

    Grandad
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