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Projectile motion: Finding flight distance with air resistance

  1. Sep 19, 2012 #1
    1. The problem statement, all variables and given/known data
    A ball of mass 9N is shot from a slingshot at an angle of 60° from the ground. The slingshot is sitting 1m above the ground. The elasticity of the slingshot is k = 700N/m. Take gravity = 10m/s^2

    Air resistance must be taken into account also. Use the formula D = ( C*P*(U^2)*A )/2
    D = Drag
    C = 1
    P = 1.2
    U = 13.94
    A = 0.03142

    How far (in the x direction) has the ball travelled when it hits the ground??


    2. Relevant equations

    F = ma
    E = 0.5mv^2
    d = vt
    d = vt + 0.5at^2
    D = ( C*P*(U^2)*A )/2 (D = Drag)

    3. The attempt at a solution

    The following calculations have already been found:

    Initial force in Ball = 350N
    Initial Energy in Ball = 87.5J

    Time of flight without air resistance = 5.5sec
    X-distance travelled without air resistance = 17.4m

    Drag = 3.66 kg/s

    I don't know how to apply the air resistance (drag) formula/calculation to what I have found.
     
  2. jcsd
  3. Sep 19, 2012 #2
    This is quite hard as a problem. A 1D problem with quadratic drag could be solved analytically, but in 2D and higher, as far as I know, it can only be solved numerically.
     
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