1. What is the Projectile Trajectory Equation?

The projectile trajectory equation calculates the height (y) of a projectile at a given distance (x) when launched at a specific angle (θ) and velocity (v), accounting for gravity (g). It's essential for understanding pellet gun ballistics.

2. How Does the Calculator Work?

The calculator uses the projectile trajectory equation:

Where:

• \( x \) — Horizontal distance (meters)
• \( \theta \) — Launch angle (radians)
• \( v \) — Initial velocity (m/s)
• \( g \) — Acceleration due to gravity (9.81 m/s²)
• \( y \) — Projectile height at distance x (meters)

Explanation: The equation accounts for both the vertical component of the initial velocity and the effect of gravity on the projectile.

3. Importance of Ballistic Calculations

Details: Accurate trajectory calculations are crucial for pellet gun accuracy, range estimation, and safety considerations when target shooting or hunting.

4. Using the Calculator

Tips: Enter distance in meters, angle in radians (0 to π/2), velocity in m/s, and gravity in m/s² (default 9.81). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: How do I convert degrees to radians?
A: Multiply degrees by π/180 (or use radians = degrees × 0.0174533).

Q2: What's a typical pellet gun velocity?
A: Most pellet guns have muzzle velocities between 150-300 m/s, depending on power and pellet weight.

Q3: Why does angle matter in trajectory?
A: The launch angle determines the balance between horizontal distance and flight time, affecting the projectile's path.

Q4: Does air resistance affect the calculation?
A: Yes, this simplified equation ignores air resistance, which can significantly affect pellet trajectory in real-world conditions.

Q5: What's the maximum range angle?
A: Without air resistance, maximum range occurs at 45° (π/4 radians). With air resistance, it's typically lower.