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If a projectile is launched from a platform 30 feet high with an initial velocity of 128 feet per second, then the height of the projectile at t seconds is given by s(t) = –16t2 + 128t + 30 feet.

(a) At what time does the projectile attain its maximum height? Show some work.






(b) What is the maximum height attained by the projectile? Show some work.

  • math -

    s(t) = –16t^2 + 128t + 30
    can do this with or without calculus
    using calculus
    ds/dt = -32 t + 128
    = 0 at max height
    32 t = 128
    t = 4 seconds
    for max height
    s(4) = -16(16) +128(4) + 30
    s(4) = 286
    without calculus find vertex of parabola
    16 t^2 -128 t = -s+30
    complete square
    t^2 - 8t = -(1/16)s + (30/16)
    t^2 - 8 t + 16 = -(1/16)s + 15/8 + 16
    (t-4)^2 = etc
    so vertex at t = 4

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