Results 1 to 4 of 4

Math Help - Velocity and maximum height

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    3

    Velocity and maximum height

    A ball is thrown upward from a height of 32 ft with an initial velocity of 16 ft/sec. Find a function that gives the position of the ball at time t. What is the maximum height the ball will reach? [Recall: a(t)= -32 ft/sec squared].

    I need some help answering this for a test I took. We get points back on our exams if we correct our mistakes. Thanks guys.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Dec 2008
    Posts
    228
    height(t) = 0.5a^2 + vt + initial height (standard height equation)

    a = acceleration (-32 ft/sec^2)

    v = initial velocity

    Differentiate, find critical number, then use either the first or second derivative test to find the maximum height.

    Edit: don't bother using the derivative tests because there's only one critical number lol.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2009
    Posts
    3
    So the function that gives the position at time t would be

    0.5(-32 ft/sec^2) + (16 ft/sec)(t) + 32 ft ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Apr 2009
    Posts
    166
    \int a(t)dt = v(t)
    \int -32dt = -32t + C

    C = Initial velocity = 16

    \int v(t)dt = s(t)
    \int (-32t + 16)dt = -16t^2 + 16t + C

    C = initial height = 32

    s(t) = -16t^2 + 16t + 32

    Maximum height can be found by calculating t when velocity changes from positive to negative.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. what is the maximum height...
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 11th 2011, 07:40 AM
  2. Replies: 11
    Last Post: April 15th 2011, 12:34 PM
  3. Finding a maximum height. (Polynomial function)
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 7th 2011, 02:39 PM
  4. Applications of Calculus - maximum height
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 24th 2010, 03:42 AM
  5. Projectile motion - maximum height
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: June 8th 2009, 03:54 AM

Search Tags


/mathhelpforum @mathhelpforum