The only trajectory problem on my whole SI sheet (trajectory) I cannot do!

  1. 1. The problem statement, all variables and given/known data
    This a trajectory problem. A ball is launched from ground level at a unknown angle. ( ∅o= ? ) at an unknown velocity ( Vo = ? )

    The ball travels 20 meters in the x direction and 25 meters up in the y direction. At this point (20,25) the ball hits a wall and a -45 angle below the horizon. Find the initial velocity ( Mag and direction ) and the speed when the ball hits the wall

    2. Relevant equations

    the only equations we have been given are

    Vyfinal = Vo( Sin ∅o) - gt
    Δ Y = Vo( Sin ∅o) - 1/2g (t)^2

    ΔX = Vo(cos ∅) (t)

    Vo( Cos ∅o) = Vf(Cos ∅o)

    Xmax = (Vo^2 * (Sin 2∅))/ g


    3. The attempt at a solution

    I cannot post all my notes. I have finished, and double checked all my other answers on 2 whole trajectory work sheets. But I cannot for the life of me figure out how to find the initial angle as a function of the final angle again the change in distance.
    I have even tried switching the whole problem around and shooting at 45° from 25 meters up and I still cannot find a result that works.

    I have done probably 10-11 different tries of canceling out different variables (especially Vo and Vf and T) and finding them as products or sums of other variables, but I can never find a way to get the original y velocity or the orignal x velocity.

    I do know that when the ball hits the wall the Y velocity is = to the -(x velocity), because tan-1 45° = -1 (-y/x)

    I have spent over 2 hours on this problem and I have searched the interwbs for help but I cannot for the life of me figure out how to find the original angle if I know the final angle but don't know either the final or intial x or y velocities. I also don't know the time

    I really, really don't like asking for answers to problems because I really like sitting down with a cup of joe and figuring it out for myself and actually learning, but I literally have grown some grey hairs and ruined my weekend over the amount of stress I have experienced over this problem, and I would really really appreciate if someone could answer this one if not give me a HUGE hint
     
  2. jcsd
  3. If the ball hits the wall at an angle of 45° after travelling 25m upwards, what does that tell you about what the maximum height reached would have been if the wall was not present?
     
    Last edited: Mar 10, 2012
  4. NascentOxygen

    Staff: Mentor

    Should be Δ Y = Vo( Sin ∅o)t - 1/2g (t)^2
     
  5. PeterO

    PeterO 2,319
    Homework Helper

    The parabolic path followed passes through 0,0 and 20,25, and the gradient at (20,25) is -1
    The second derivative anywhere is -9.8

    Surely if you put all that together the answer can be extracted
    That enables you
     
  6. I typed this very late last night, I promise you that that "t" was there in every single one of my equations. I lose track of variables when I have to keep typing out all the little subscripts and figures, sorry.

    it hits the wall at a -45 degree angle after it maximum y value
     
  7. "The parabolic path followed passes through 0,0 and 20,25, and the gradient at (20,25) is -1
    The second derivative anywhere is -9.8

    Surely if you put all that together the answer can be extracted
    That enables you"


    I just started calculus 2 weeks ago. I am decent with derivatives but to be honest I have never done a lick of integration, which is what I would need to go from having the derivative to the original right?
     
  8. Define a time, t, for yourself, that being how long it takes to get to the wall. So we know at time t its horizontal and vertical velocities are both 20/t.

    Now ask a different question - with initial velocities 20/t both horiz and vertical, from a height 25, what angle will its flight intersect the horizontal if it goes from there?
     
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