calculus

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Wiley jumps straight up in the air from the edge of a cliff so that when he comes down he falls off the cliff. The cliff is 40 feet off the ground. His height t seconds after he jumps is s= -16t2 + 12t + 40.What is the maximum height? What is his maximum velocity?

  • calculus -

    ds/dt = -32t + 12
    = 0 for a max of s
    32t = 12
    t = 12/32 sec = 3/8 sec
    for that time
    s = -16(9/64) + 12(3/8) + 40
    = 169/4 or 42.25 ft above the base of the cliff

    when he hits the ground, s = 0
    -16t^2 + 12t +40=0
    divide by -4
    4t^2 - 3t - 10 = 0
    (t-2)(4t+5) = 0
    t = 2 or t = -5/4, but t > 0
    so he will hit the ground after 2 seconds

    ds/dt = -32t+12
    when t=2
    ds/dt = -32(2) + 12 = -52 ft/sec
    the negative indicates a downward direction, he is falling

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