A ball is launched from the ground with a horizontal speed of 30 m/s and a vertical speed of 30 m/s. What far vertically will it travel befo

Question

A ball is launched from the ground with a horizontal speed of 30 m/s and a vertical speed of 30 m/s. What far vertically will it travel before hiting the ground A. 40 m B. 30 m C. 60 m D. 50 m

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Calantha 4 years 2021-08-11T18:52:37+00:00 1 Answers 10 views 0

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  1. Bo
    0
    2021-08-11T18:53:37+00:00
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    Answer:

    First, let’s think in the vertical problem:

    The acceleration will be the gravitational acceleration:

    g = 9.8 m/s^2

    a = -9.8 m/s^2

    For the velocity, we integrate over time:

    v(t) = (-9.8 m/s^2)*t + v0

    Where v0 is the initial velocity, in this case  v0 = 30m/s.

    v(t) =  (-9.8 m/s^2)*t + 30m/s

    Now, for the position we integrate again over time, and get:

    P(t) = (1/2)*(-9.8 m/s^2)*t^2 + 30m/s*t + p0

    Where p0 is the initial position, as the ball is launched from the ground, we can use p0 = 0m

    p(t) = (-4.9m/s^2)*t^2 + 30m/s*t

    Now, the maximum vertical height is reached when:

    v(t) = 0m/s = -9.8m/s^2*t + 30m/s

    t = 30m/s/9.8m/s^2 = 3.06s

    Now we can evaluate the vertical position in t = 3.06s

    p(3.06s) = (-4.9m/s^2)*(3.06)^2 + 30m/s*3.06 = 62m

    So, rounding down, the correct option is: C. 60 m

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