Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By skeeter

Thread: projectile

  1. #1
    Senior Member
    Joined
    May 2016
    From
    england
    Posts
    356
    Thanks
    2

    projectile

    a projectile is fired with velocity u at an angle a above the horizontal.. it lands on the same horizontal plane at point P. it lands the furthest point away on the plane. show that for the projectile to hit a point H above point P and its projected at the same angle the initial velocity must be u^2/root(u^2-gh)

    i know that the angle of elevation is 45 degrees. im trying to use ut-.5gt^2=h
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,605
    Thanks
    2367

    Re: projectile

    1) Use $u$ to determine the range of the first projectile

    2) write the equation of motion for the second projectile that travels with initial speed $w$

    3) a point on the curve given by (2) is (range, H), thus you have two equations, one in each of the components

    4) solve these two equations for $w$ and $t$

    5) note that you want the answer where $t>0$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    15,959
    Thanks
    3580

    Re: projectile

    For the initial projectile landing at point $P$ ...

    $\Delta x = \dfrac{v_0^2 \sin(2\theta)}{g} = \dfrac{u^2}{g}$

    The second projectile launched at the higher speed (call it $v$) will have the same value for $\Delta x$ when it reaches the height, $H$, directly above point $P$.

    $\Delta x= v\cos(45) \cdot t = \dfrac{u^2}{g} \implies t = \dfrac{u^2\sqrt{2}}{gv}$

    substitute the above expression for $t$ into the equation $H=v\sin(45) \cdot t - \dfrac{1}{2}gt^2$, then solve for $v$.
    Thanks from markosheehan
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    May 2016
    From
    england
    Posts
    356
    Thanks
    2

    Re: projectile

    thanks i get it now. i worked the distance in the x direction in a different way though
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. projectile
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: Feb 13th 2017, 02:41 PM
  2. projectile
    Posted in the Advanced Applied Math Forum
    Replies: 6
    Last Post: Jan 29th 2017, 07:45 AM
  3. Projectile
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: Mar 22nd 2010, 12:41 PM
  4. projectile
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Mar 7th 2009, 06:18 AM

/mathhelpforum @mathhelpforum