Conceptual Dynamics - Independent Learning

Projectile Motion

 

Solving projectile problems

 

Falling objects have certain special properties that help us solve projectile motion problems.

 

 

  1. The x and y-components of motion are independent.

    2.  

    The projectile motion may be broken up and analyzed as two rectilinear problems using the following equations.

     

    vo = vxo i + vyo j = v(cos(θ) i + sin(θ) j)

     

    x-direction y-direction
    vx = dx/dt vy = dy/dt
      ay = dvy /dt
      ay dy = vy dvy

     

    If a man shoots a bullet from the same height and at the same time that a woman shoots an arrow, which will hit the ground first? Neglect air resistance and assume that they both shoot horizontally.

     

     

     

     

     

  2. The x-direction velocity is constant.

    3.  

    If we neglect air resistance, the x-direction velocity does not change while the projectile is aloft.

     

    x-direction y-direction
    vx = dx/dt = constant
    ax = 0
    x = xo + vxot

     

  3. The y-direction acceleration is constant.

    4.  

    This means the y-direction velocity changes continuously throughout the projectile's motion.

     

    x-direction y-direction
    ay = dvy/dt = -g
    vy = dy/dt = vyo - gt
    y = yo - vyot - (gt 2/2)

     

  4. The y-direction velocity at the apex of motion is zero.

    5.  

    The apex is the top of the projectile's motion. At this point the projectile changes directions. Therefore, the velocity in the y-direction at the apex must equal zero.

     

    x-direction y-direction
    vy,apex = 0

     

  5. If the starting height of the projectile is the same as the ending height, then the motion of the projectile is symmetric.