L8 - Projectile Motion

• Why is Projectile Motion Important to Understand?

  • Flight phase in sport; CoM follows projectile motion
  • Optimising/predicting flight
• Why is Projectile Motion Important to Understand?

  • Flight phase in sport; CoM follows projectile motion
  • Running, jumping - when you leave the ground or an object does (throwing) → want to know what body/object is doing in the air
• Why is Projectile Motion Important to Understand?

  • Optimising/predicting flight
  • With take off speed/velocity; launch direction & angle
  • Work on aspects of technique
  • Lots of applications for this
• Trajectory of a Projectile:

  • If we ignore air resistance, the flight of a projectile is a parabola
  • Parabola: near right & left from its apex & follows a curve path (inverted U)
  • Ascending & descending parts of trajectory are symmetrical
  • When reaches same height has same velocity just in different direction
• Trajectory of a Projectile:

  • We know:
  • velocity apex, y = 0
  • When reaches apex vertical is 0
  • initial velocity, y = -final velocity, y
  • Important as ask how high apex, need to know initial launch & final
  • y = vertical
• Factors Influencing Projectiles -Angle:

  • v = projectile velocity vector
  • No ideal, there is an optimal of matching with the angle
  • 𝜽 = projectile angle
  • h = projection height
• Factors Influencing projectiles - Velocity:

  • Velocity vector has a horizontal (vx) & a vertical (vy) component
  • Describes launch
  • How much up & how much to the right
  • During flight, vy decreases (-) at a rate of 9.81 m/s every second
  • Doesn't hold same velocity the whole time
• Factors Influencing Projectiles - Velocity:

  • vy (vertical velocity) determines the change in height & flight time
  • Affects how long in the air
  • vx (horizontal velocity) is constant & is needed to determine range
  • As ignoring air resistance
  • In terms of acceleration vy is -9.81 m/s^2; vx acceleration is ALWAYS 0
• Factors Influencing Projectile Height:

  • Launch height affects range of projection
  • To increase range:
  • Lower launch angle with increase projection height
  • Pos = Throw from higher than landing height goes further & landing angle steeper
  • Higher launch angle with decrease projection height
  • Neg = Landing higher/throwing up onto something (eg basketball shot)
  • Trade off bw/ velocity & angle
• Factors Influencing Projectile Height:

  • x & y independent when drop straight down bounce the same to as if have horizontal component or not (a push) - have to break vectors into their components
  • Parabola follows the centre of mass
  • High jump → launch velocity (y); & height of CoM (taller, put arms up shifts CoM up), & angle to get over the bar → centre of mass could be under bar & still get over
• 3 Equations of Constant Acceleration:

  • Vertical acceleration = -9.81 m/s^2 → gravity
  • Horizontal acceleration = 0 m/s^2 → ALWAYS
• 3 Equations of Constant Acceleration:

  1. vf = vi + aΔt
  2. Δ s = viΔt + 1/2aΔt^2 → horizontal ONLY
  3. vf^2 = vi^2 + 2aΔs
• 3 Equations of Constant Acceleration:

  • Final doesn’t always mean where it lands; final can be peak height
  • Initial = launch
  • Relationship bw/ these that give equations their value
  • Depends what you have, what equation you use
  • Use only with vertical OR horizontal; 1 or other not a mix
  • Only use 1 component
  • Equation 2. only relevant for horizontal