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Get Projectile hit moving target

  1. Jan 30, 2008 #1
    Hello i need this för a coding project im currently occupying myself with =)

    ok so the system is in a 2D space, the projectile starts at a height H and is supossed to hit target T. the targets y.coord is constant Ty but his x has a speed Tv towards the projectiles start. the target starts at a distance D from the projectile. the projectile has a given starting speed of Pv0 and the angle A.

    oh right and gravity is affecting the projectile =)

    SO! what i need is a formula that can tell what angle I need to hit the target.

    Thanks in advance
    Last edited: Jan 31, 2008
  2. jcsd
  3. Jan 31, 2008 #2
    Was this too difficult or is there not enough information??
  4. Jan 31, 2008 #3


    Staff: Mentor

    You can write an expression for the location of the projectile as a function of t and the angle, and you can write an expression for the location of the target as a function of t. Set them equal to each other and you have an equation describing when they collide. That leaves 2 equations in 2 unknowns so you can solve for t and the angle.
  5. Feb 3, 2008 #4
    This is how far ive got. Im stuck so can you please say how i can solve the rest or if there is some other way to solve it.
    it might be quite hard to follow on screen so i suggest you follow my calculations on paper.

    the target's y coordinate is always 0

    Tv = the target's X velocity (speed)
    Pv = the projectile's velocity

    d0 = the target's x coordinate at t=0
    y0 = the projectile's y coordinate at t=0

    Pvx = Pv * cosa
    Pvy = Pv * sina +gt

    Px = Pv *cosa *t
    Tx = d0 + Tv *t
    Py = y0 + Pv* sina + (g*t^2) / 2
    Ty = 0

    Tx = Px
    Ty = Py

    (1.) d0 + Tv *t = Pv *cosa *t
    (2.) 0 = y0 + Pv* sina + (g*t^2) / 2

    (1.) cosa^2 = ( ( d0 + Tv *t )/(Pv * t) )^2
    (2.) sina^2 = (( -y0 -(g*t^2) / 2 ) / Pv)^2

    cosa^2 + sina^2 = 1
    (1.) + (2.) = 1

    ( ( d0 + Tv *t )/(Pv * t) )^2 + (( -y0 -(g*t^2) / 2 ) / Pv)^2 = 1
  6. Feb 3, 2008 #5


    Staff: Mentor

    You shouldn't try to solve this by hand. You should either plug the equations into a symbolic math package, like Mathematica, or you should solve it numerically. Just for grins I used Mathematica. I had these two equations describing repectively the x and y coordinates of the collision:

    T0x + t Tvx == Pv t Cos[a]
    2 P0y + g t^2 + 2 Pv t Sin[a] == 0

    Solving this simple appearing system for t and a resulted in 8 roots, each one of which was over 100 pages of output.

    You could probably solve this a more clever way to get fewer roots and slightly simpler expressions. One typical way is to not solve for the angle but rather the x and y components. But you would never get something truly simple. If you are coding I would recommend using a numerical solver. There are lots of packages available, many for free.
    Last edited: Feb 3, 2008
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