Results 1 to 3 of 3

Math Help - Instantaneous Rate of Change of Height

  1. #1
    Junior Member
    Joined
    Mar 2010
    Posts
    56

    Red face Instantaneous Rate of Change of Height

    A soccor ball is kicked into the air. The polynomial function f(t) = -4.9^2 +16t + 1, where the f(t) represents the height in metres at t seconds models this scenario.
    Determine the instantaneous rate of change of height at 1 second, 2 seconds and 3 seconds.


    Im thinking I use this:
    f ' (1) = lim_____ f(1 + h) - f(1)
    ______ h→0______h

    and so forth for 2 seconds, and 3 seconds..

    But I got 87.71 m/s for 1 second - doesn't seem right?

    Help lol thanks in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Educated's Avatar
    Joined
    Aug 2010
    From
    New Zealand
    Posts
    430
    Thanks
    12
    Is it supposed to be: f(t) = -4.9t^2 +16t + 1

    \lim \limits_{h \rightarrow 0} \dfrac{f(1+h) - f(1)}{h}

    \lim \limits_{h \rightarrow 0} \dfrac{[-4.9(1+h)^2 +16(1+h) +1] - [-4.9(1)^2 +16(1) +1]}{h}

    \lim \limits_{h \rightarrow 0} \dfrac{-4.9 -4.9h^2 - 9.8h +16+16h +1 + 4.9 -16 -1}{h}

    \lim \limits_{h \rightarrow 0} -4.9h +6.2 = 6.2

    Now can you do it for 2 seconds and 3 seconds?


    The easier way would be to straight differentiate it to get the rate of change.

    f(x) = x^n
    f'(x) = nx^{n-1}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2010
    Posts
    56
    I did what you did, but I got a huge number. Need to triple check my numbers then..
    I haven't learned straight differentiate yet.. but soon
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Instantaneous Rate of Change
    Posted in the Algebra Forum
    Replies: 8
    Last Post: January 14th 2010, 03:29 PM
  2. instantaneous rate of change
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: September 27th 2009, 09:40 AM
  3. Instantaneous Rate of Change
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 30th 2009, 12:11 PM
  4. Instantaneous rate of change?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 3rd 2009, 09:09 AM
  5. Instantaneous rate of change
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 25th 2008, 06:44 PM

Search Tags


/mathhelpforum @mathhelpforum