Projectile Motion: Range, Time-of-Flight, Maximum Height

Understanding Projectile Motion

Projectile motion involves objects that are thrown or launched into the air and are subject to gravity. Key aspects include the range, time-of-flight, and maximum height.

Key Concepts

• Range: The horizontal distance a projectile travels before landing.
• Time-of-Flight: The total time a projectile is in the air.
• Maximum Height: The highest vertical position reached by a projectile.

Equations

• Range (R):

  $$R = \frac{v_0^2 \sin(2\theta)}{g}$$

  Where:
  • $v_0$ = initial velocity
  • $\theta$ = launch angle
  • $g$ = acceleration due to gravity (approximately $9.8 \text{ m/s}^2$)
• Time-of-Flight (T):

  $$T = \frac{2v_0 \sin(\theta)}{g}$$

• Maximum Height (H):

  $$H = \frac{v_0^2 \sin^2(\theta)}{2g}$$

Worked Example