1. What is Projectile Range?

The projectile range is the maximum horizontal distance traveled by an object in projectile motion. It depends on the initial velocity, launch angle, and gravitational acceleration.

2. How Does the Calculator Work?

The calculator uses the range equation:

Where:

• \( R \) — Range (meters)
• \( v \) — Initial velocity (m/s)
• \( g \) — Gravitational acceleration (9.81 m/s² on Earth)
• \( \theta \) — Launch angle (degrees)

Explanation: The equation shows that range increases with the square of velocity and reaches maximum at 45° launch angle.

3. Importance of Range Calculation

Details: Calculating projectile range is essential in physics, engineering, ballistics, and sports science to predict where launched objects will land.

4. Using the Calculator

Tips: Enter velocity in m/s, angle in degrees (0-90), and gravitational acceleration (9.81 m/s² for Earth). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What angle gives maximum range?
A: On level ground with no air resistance, 45° gives maximum range for a given velocity.

Q2: How does air resistance affect range?
A: Air resistance reduces range, especially at higher velocities, and changes the optimal angle to less than 45°.

Q3: Does mass affect projectile range?
A: In vacuum, no. With air resistance, heavier objects generally have greater range as they're less affected by drag.

Q4: How to calculate range on an inclined plane?
A: The equation becomes more complex, requiring adjustment for the slope angle.

Q5: What's the range at 0° or 90°?
A: At 0° (horizontal), range is zero (object falls straight down). At 90° (vertical), range is zero as object goes straight up and down.