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calculus

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use a(t) = -32 ft per second squared as the acceleration due to gravity.An object is thrown vertically downward from the top of a 480-ft building with an initial velocity of 64 feet per second. With what velocity does the object hit the ground?

This type of problem always shows up on my test and I always get it wrong. Can someone show me how to do it? Thanks.

  • calculus -

    At this point you should know that
    if s(t) is the height obtained, then
    v(t) , or velocity, is s'(t) and
    a(t) , the acceleration, is v'(t) or s''(t)

    Also having done some of these, by now you should know that for the above,
    s(t) = -16t^2 + 64t + 480 and
    v(t) = -32t + 64

    so when it hits the ground, isn't s(t) = 0 ??
    so
    -16t^2 + 64t + 480 = 0
    t^2 - 4t - 30 = 0
    t = 2 ± √34 , we can reject the negative value
    t = 2+√34

    sub that into v(t) and you are done

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