MODULE 1

• The purpose of this module is to help you understand the horizontal and vertical motion of a projectile and the relationship between the angle of release and the height and the range of the projectile
• This module contains one lesson: Projectile Motion
• After going through this module, you are expected to

  • Describe the horizontal and vertical motion of a projectile
  • Investigate the relationship between the angle of release and the height and range of the projectile
• Projectile


  An object thrown with an initial velocity and acted upon by the earth's pull of gravity
• Trajectory


  The curved path taken by the projectile
• Range


  The horizontal distance traveled by a projectile within the total time of its flight
• Projectile motion


  • Combination of vertical and horizontal motion which are independent of each other
  • Horizontal motion is constant while vertical motion is changing
• Equations of projectile motion

  1. Vertical motion: h=gt^2/2

  2. Horizontal motion: R=vxt
• Projectile thrown at an angle

  Horizontal velocity remains constant, vertical velocity changes
• Maximum height


  When vertical velocity is zero
• Projectile motion at complementary angles have the same range
• Sample problem: Projectile thrown at 20 degrees


  Given: Vi=50m/s, θ=20°

  Formula: R=vi^2sin2θ/2g

  Solution: R=164m
• Height of the projectile


  h=(visinθ)(t) - (1/2)gt^2
• Range R

  R= vi^2sin 2θ/g
• The range R is calculated using this equation and is applicable to all values of θ
• An object that is thrown at 30° into the air will have the same range when it is thrown at 60°
• The object when thrown at 70°, 20°, and 10° will have the same ranges as it was thrown in 20°, 70°, and 80° respectively
• The maximum range obtained is 45°
• Sample Problem: What must be the horizontal distance of the ball if it is thrown with initial velocity of 50.0 m/s at an angle of 20.0°?

  1. Given: Vi = 50.0m/s, θ = 20.0°, Unknown: R = ?

  2. Formula: R= vi^2sin2θ/2g

  3. Solution: R= (50m/s)^2sin2(20°)/(9.8m/s^2)

  4. Answer: R = 164 m
• Projectile Motion and Complementary Angles
• When an object is thrown at 15°, 30°


  It will have the same range
• The launch angle that will have the same range as a projectile launched at 20°

  70°
• In the absence of air resistance, the angle to get the maximum range is 45°
• In the Javelin throw event, the angle to attain the farthest distance is 45°