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2 September, 20:44

At a particular instant, a hot air balloon is 100 m in the air and descending at a constant speed of 2.0 m/s. At this exact instant, a girl throws a ball horizontally, relative to herself, with an initial speed of 20 m/s. When she lands, where will she find the ball? Ignore air resistance.

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  1. 2 September, 21:03
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    Use this kinematics equation to the describe the vertical motion of the ball as a function of time:

    H (t) = X + Vt + 0.5At²

    H (t) is the height of the ball

    X is the initial height of the ball

    V is the initial vertical velocity of the ball

    A is the vertical acceleration of the ball

    Given values:

    X = 100m

    V = - 2m/s

    A = - 9.81m/s² (constant acceleration due to gravity near the surface of the earth)

    Plug in the values:

    H (t) = 100 - 2t - 4.905t²

    To find a time t for when the ball hits the ground, plug in H (t) = 0 and solve for t:

    100 - 2t - 4.905t²

    t = 4.316s, - 4.724s

    Reject the negative value because this doesn't make sense in the context of the question.

    t = 4.316s

    For the ball's horizontal motion under constant velocity:

    X = VΔt

    X is the horizontal distance traveled by the ball

    V is the ball's velocity

    Δt is the elapsed time

    Given values:

    V = 2.0m/s

    Δt = 4.316s (from previous work)

    Plug in and solve for X:

    X = 2.0*4.316

    X = 8.632m

    The girl will find the ball 8.632m from where her hot air balloon will land.
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