Calculus

1.if a ball is thrown into the air with a velocity of 35ft/s, it's height in feet after t seconds is given by y=35t-10t^2. Find the averag velocity for the time period beginning when t=4 and lasting 0.05s.
2.if a ball is thrown into the air with a velocity of 30ft/s, it's height in feet after t seconds is given by y=30t-20t^2. Find the instantaneous velocity when t=3

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asked by Jacke
  1. Last time I was on this earth, gravity would cause an equation of the type
    y = -16t^2 .....
    So assuming you have a typo and it should have been
    y = 35t - 16t^2
    Second problem:
    the ball would not be in the air for 4 seconds,
    so your whole first question is actually just gibberish.
    Once you fix it, find y when t = 4
    find y when t = 4.05
    evaluate: ( y(4.05) - y(4) )/.05

    2. same thing here,
    after 3 seconds the ball has reached the ground, and no longer has any velocity

    if we ignore reality,
    dy/dt = 30 - 40t
    when t = 3
    dy/dt = 30 - 120 = -90 ft/s


    1.
    when t=4, y = 35(4) - 16(16) = -20

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    posted by Reiny
  2. There is no error in the problem.

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    posted by Jacke
  3. I see the typo as specifying feet. In metric units, g=9.8, or roughly 10, so Jacke, redo the calculations, with g=10 and get the correct answer.

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    posted by Steve
  4. Is it ok if I get a negative answer???

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    posted by Jacke
  5. OK thanks I got it

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    posted by Jacke

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