projectile angle

• Projectile motion is the combination of horizontal motion with constant velocity and vertical motion with constant acceleration
• Projectile motion launched at an angle

  • Horizontal velocity (VX) is constant
  • Vertical velocity (VY) decreases as projectile rises
  • Vertical velocity is zero at maximum height
  • Vertical velocity increases as projectile returns to ground
• Variables involved in projectile motion launched at an angle

  • Horizontal component
  • Vertical component
• An object is projected from rest at an upward angle Theta
• Initial velocity can be resolved into horizontal and vertical components
• Horizontal velocity is constant due to gravity
• Time to reach maximum height is same as time to return to launch point
• Initial upward velocity is same as final velocity when returning to original height
• Angle of 45 degrees results in maximum range
• Angle of 75 degrees results in maximum height
• Angles of 30 and 60 degrees have the same range
• Angles of 15 and 75 degrees have the same range
• As angle of launch increases, vertical displacement increases
• At maximum height, vertical velocity is zero
• Time to reach maximum height is half of total time of flight
• Theta

  Numerical value in degrees expressing the orientation of a projectile
• Solving for maximum height of projectile

  1. Use formula: VI * sin(Theta)^2 / (2 * g)

  2. Substitute given values

  3. Simplify units
• Solving for horizontal displacement (range) of projectile

  1. Use formula: VI * cos(Theta) * t

  2. First solve for total time of flight

  3. Then calculate horizontal displacement
• Baseball player hits a long home run with ball leaving bat at 25 degrees and 30 m/s
• Maximum height reached by ball is 8.20 meters
• Horizontal displacement (range) of ball is 70.42 meters