Projectile Motion Overview

Overview

This lesson covers projectile motion launched at an angle, focusing on the relationship between the angle of release and the projectile's height and range.

Basics of Projectile Motion

• Projectile motion combines constant horizontal velocity and constant vertical acceleration due to gravity.
• The horizontal component (VX) has zero acceleration, so velocity is constant.
• The vertical component's acceleration is always 9.8 m/s² downward due to gravity.
• The trajectory of a projectile is parabolic.

Components of Motion and Velocity

• At launch, the initial velocity (VI) splits into horizontal (VX) and vertical (VY) components.
• VX remains unaffected by gravity and is constant.
• VY decreases as the object rises, becomes zero at the maximum height, and increases downward as it falls.
• The time to reach maximum height equals the time to descend back to the launch level.
• The initial upward velocity equals the final downward velocity at the same height.

Effects of Launch Angle

• The range (horizontal displacement) is greatest at a 45° launch angle.
• Maximum height is achieved at higher angles, like 75°.
• Pairs of complementary angles (e.g., 30° and 60°, 15° and 75°) provide the same range.
• Increasing the launch angle increases vertical displacement.
• At the highest point, the vertical velocity is zero.
• Time to maximum height is half the total flight time.

Example Problem: Baseball Home Run

• Initial velocity (VI): 30 m/s, launch angle: 25°, gravity: 9.8 m/s².
• Maximum height formula: ( H = \frac{(VI \cdot \sin \theta )^2}{2g} )
  • Substituting values: ( H = 8.20 ) meters.
• Total flight time formula: ( t = \frac{2 \cdot VI \cdot \sin \theta }{g} )
  • Calculated time: ( t = 2.59 ) seconds.
• Range formula: ( DX = VI \cdot \cos \theta \cdot t )
  • Calculated range: ( DX = 70.42 ) meters.

Key Terms & Definitions

• Projectile Motion — Motion of an object thrown into the air, affected only by gravity and air resistance.
• Trajectory — The path a projectile follows, typically a parabola.
• Range — The horizontal distance a projectile travels.
• Complementary Angles — Two angles whose sum is 90°, resulting in the same range for projectile motion.
• Maximum Height — The highest point a projectile reaches in its path.

Action Items / Next Steps

• Review and practice solving projectile motion problems using the provided formulas.
• Prepare for the next lesson on related physics concepts.