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Finding the Angle in Projectile Motion

  1. Jan 22, 2009 #1
    1. The problem statement, all variables and given/known data

    Hello, I am attempting to derive an equation for some pretty specific needs. The equation I need is one that solves for the angle needed to launch a projectile at a given velocity to an object at a given distance and height different from launcher. The catch is that I would like to include the acceleration due to air resistance (which I can find later and input) as an acceleration in the x direction.

    The goal is to solve for theta (I will use an o)

    2. Relevant equations

    The only variables that can be present in the equation are:
    ax, ay (gravity), x, y, v (velocity launched at, actually, it is the speed, I don't know the angle)

    The equations I have been attempting to use are:

    y = vy*t + (g/2)*t^2
    x = vx*t + (a/2)*t^2
    v = sqrt(vx^2 + vy^2)
    sin o = vy/v
    cos o = vx/v

    3. The attempt at a solution

    I keep trying to derive but keep ending up circling (deriving until I accidentally reach a variable I tried to get rid of earlier). Does anyone have an equation already derived they could show me that they could also explain how they derived, or know how I could go about deriving my goal equation successfully? Or any other formulae I should be using?

  2. jcsd
  3. Jan 22, 2009 #2


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    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Robotics 1764! Welcome to PF! :smile:

    (air resistance would never be like that, but anyway …)

    Hint: since you have constant acceleration in both the x and y directions, try combining them (accelerations obey the vector law of addition, of course) into a single acceleration, and then use coordinates parallel and perpendicular to that direction. :wink:
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