Results 1 to 8 of 8

Math Help - pellet gun physics problem

  1. #1
    Senior Member
    Joined
    Jan 2007
    Posts
    477

    pellet gun physics problem

    any help with this is greatly appreciated please.

    A pellet gun is fired straight downward from the edge of a cliff that is 16 m above the ground. The pellet strikes the ground with a speed of 26 m/s. How far above the cliff edge would the pellet have gone had the gun been fired straight upward?
    how many meters?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    It's a standard setup. You must know only these:

    a(t) = -g -- g is acceleration due to gravity

    v(t) = -g*t + v0 -- v0 is the initial velocity that we are not given.

    s(t) = -g*t^2 + v0*t + h0 -- h- is the initial height that we are given.

    So,

    s(t) = -g*t^2 + v0*t + 16 m

    It hits the ground when? s(t) = 0

    0 = -g*t^2 + v0*t + 16 m

    This gives the slightly untidy t_{impact} = \frac{1}{g}\left(v_{0}+\sqrt{v_{0}^{2}+32*g* m}\right).

    There's another solution, but it's negative and I'm sure we don't want that.

    We are given the velocity on impact.

    v(t_{impact}) = 26 m/s

    That should lead you to the initial velocity. (Hint: I get a little over 19 m/s)

    Once you have that, you are on your way to a simple solution of the maximum of a parabola.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,939
    Thanks
    338
    Awards
    1
    Please let me add two things to TKHunny's post.

    Specifically there is a coordinate system defined here that has an origin at the bottom of the cliff, and the positive s direction is defined to be upward.

    (I feel it is crucial to make a mention of these things. )

    -Dan
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    Kinetic energy generates a velocity with which the projectile leaves the barrel while the ballistic coefficient and sectional density determine the damage to the target.
    Therefore, guns dont kill people, physics does.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,939
    Thanks
    338
    Awards
    1
    Quote Originally Posted by galactus View Post
    Kinetic energy generates a velocity with which the projectile leaves the barrel while the ballistic coefficient and sectional density determine the damage to the target.
    Therefore, guns dont kill people, physics does.
    What on Earth are you talking about??

    If someone is hit in the toe with a bullet they don't die. If they get hit in the heart, they are very likely to die.

    Thus guns don't kill people nor does physics: physiology kills people.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    For heaven's sake, it's a joke. It is a quote from John Lithgow's character on "3rd Rock from the Sun".
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,939
    Thanks
    338
    Awards
    1
    Quote Originally Posted by galactus View Post
    For heaven's sake, it's a joke. It is a quote from John Lithgow's character on "3rd Rock from the Sun".
    Ummm... My reparte was a joke as well...

    -Dan
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    Quote Originally Posted by topsquark View Post
    (I feel it is crucial to make a mention of these things. )
    Right. As soon as I walked away, I somewhat regretted two things:

    1) Lack of more clear definitions.
    2) The sign of 'g'.

    Anyway, if you can sort it out, it was worth it.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Physics Problem
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: June 6th 2010, 04:52 PM
  2. Replies: 2
    Last Post: January 10th 2009, 05:49 AM
  3. physics, acceleration, physics problem
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: September 29th 2007, 03:50 AM
  4. A physics problem
    Posted in the Calculus Forum
    Replies: 8
    Last Post: January 12th 2006, 04:47 PM
  5. Physics problem
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: December 28th 2005, 11:23 PM

Search Tags


/mathhelpforum @mathhelpforum