physical

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a ball that was projected up at an angle of θ degrees with the horizontal has a flight time of 5.0s and covers a range of 49.0 m. find (a) the time it took to reach maximum height, (b) the horizontal and vertical components of its initial velocity, (c) its initial velocity,(d) the angle θ at which it was projected, and (e) the maximum height it reached.

  • physical -

    vertical problem:
    2.5 seconds up and 2.5 seconds down
    v = Vi - 9.81 t
    at top v = 0
    so
    Vi = 9.81*2.5 = 24.5 m/s up
    h = Vi t - 4.9 t^2
    = 24.5(2.5) -4.9(6.25)
    = 61.3 - 30.6
    = 30.6 meters high at top

    horizontal problem
    49 = u (5)
    so u = 9.8 m/s

    tan theta = Vi/u = 24.5/9.8
    theta = 68.2 degrees

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