Projectile Motion

• Projectile Motion - any object that moves in two dimensions.
• Projectile - The only force is gravity.
• 2 Dimensions

  • Horizontal - Range
  • Vertical - Height
• Trajectory - curved path of the projectile.
• In studying projectile motion, we need to observe the relationship of the angle to the height and range.
• 5 Variables/Quantities

  • Angle of Projection
  • Maximum Height
  • Range
  • Time of Flight
  • Total Time of Flight
• Angle of projection - the angle between the initial velocity of an object from a horizontal plane.
• Maximum Height

  • Highest peak reached by the projectile
  • Object up = velocity decrease
  • Object down = velocity increases
• Range - horizontal distance traveled by a projectile.
• Time of Flight - time taken to reach peak
• Total time of Flight - time taken to reach the peak from the starting point to the ending point
• Symbols

  • Θ (theta) - angle of projection
  • dymax/h - height
  • Vy - peak (always 0)
  • Vi - initial velocity
  • R - range
  • Vix - Horizontal Vi
  • Viy - Vertical Vi
• Steps

  1. Identify the variables
  2. Calculate Vix and Viy
  3. Calculate time of flight
  4. Calculate total time of flight
  5. Calculate height
  6. Calculate range
• Formulas:

  • Vix = Vi x cos Θ
  • Viy = Vi x sin Θ
  • time of flight = Vy - Viy / g
  • total time of flight = time of flight x 2
  • dymax = (Vy)^2 - (Viy)^2 / 2g
  • R = Vix x total time of flight
• Relationship between the angle of projection when it comes to height and range.

  >45 degrees - height = higher ; range = shorter