1. What is Projectile Range?

The projectile range is the maximum horizontal distance traveled by a projectile when launched at a specific angle with a given initial velocity. It's a fundamental concept in physics and engineering.

2. How Does the Calculator Work?

The calculator uses the projectile range equation:

Where:

• \( R \) — Projectile range (meters)
• \( v \) — Initial velocity (m/s)
• \( \theta \) — Launch angle (degrees)
• \( g \) — Acceleration due to gravity (9.81 m/s² on Earth)

Explanation: The equation shows that range depends on the square of velocity and the sine of twice the launch angle, divided by gravitational acceleration.

3. Importance of Projectile Range Calculation

Details: Calculating projectile range is essential in fields like ballistics, sports science, engineering, and physics education. It helps predict where a projectile will land.

4. Using the Calculator

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

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: Does this account for air resistance?
A: No, this is the idealized equation without air resistance. Real-world ranges will be shorter.

Q3: What units should I use?
A: Use meters per second (m/s) for velocity, degrees for angle, and meters per second squared (m/s²) for gravity.

Q4: Why does the equation use sin(2θ)?
A: This comes from the trigonometric identity that combines the horizontal and vertical motion components.

Q5: Can I use this for objects launched from height?
A: This equation assumes launch and landing at the same elevation. Different equations are needed for uneven terrain.