1. What is Projectile Range?

The projectile range is the maximum horizontal distance traveled by a projectile when launched at an angle θ with initial velocity v₀ under constant gravity g, neglecting air resistance.

2. How Does the Calculator Work?

The calculator uses the projectile range equation:

Where:

• \( R \) — Range (meters)
• \( v_0 \) — 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 initial velocity and the sine of twice the launch angle.

3. Importance of Projectile 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 initial velocity in m/s, launch angle in degrees (0-90), and gravity in m/s² (9.81 for Earth). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What angle gives maximum range?
A: 45 degrees gives maximum range when air resistance is neglected.

Q2: Does this work for any planet?
A: Yes, just adjust the gravity value (3.71 m/s² for Mars, 1.62 m/s² for Moon).

Q3: Why doesn't mass appear in the equation?
A: Mass cancels out in the derivation, so range is independent of mass.

Q4: How does air resistance affect range?
A: Air resistance reduces range significantly, especially for fast-moving or light objects.

Q5: What's the range at 0° or 90°?
A: At 0° (horizontal launch), range is maximum. At 90° (straight up), range is 0 as the projectile lands at the launch point.