1. What is Ballistics Trajectory?

Ballistics trajectory refers to the path that a projectile follows under the action of gravity. This calculator computes both the horizontal range and vertical height of a projectile at a given time.

2. How Does the Calculator Work?

The calculator uses the following ballistics equations:

Where:

• \( v \) — Initial velocity (m/s)
• \( \theta \) — Launch angle (degrees)
• \( t \) — Time (seconds)
• \( g \) — Acceleration due to gravity (m/s², default 9.81)

Explanation: The equations account for both the horizontal and vertical components of motion, with gravity affecting only the vertical component.

3. Importance of Trajectory Calculation

Details: Understanding projectile motion is essential in fields like physics, engineering, military applications, and sports science. Accurate trajectory calculations help predict where a projectile will land.

4. Using the Calculator

Tips: Enter initial velocity in m/s, launch angle in degrees (0-90), time in seconds, and gravity in m/s². All values must be positive, with angle between 0-90 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the optimal angle for maximum range?
A: In a vacuum, 45° gives maximum range. With air resistance, the optimal angle is typically less (about 30-40° depending on velocity).

Q2: Why does height become negative?
A: Negative height values indicate the projectile has fallen below the launch elevation (ground level).

Q3: Does this account for air resistance?
A: No, these are ideal equations without air resistance. Real-world trajectories will have shorter ranges due to drag.

Q4: What's the maximum time I can calculate?
A: Theoretically until the projectile hits the ground, but extremely large times will give unrealistic results.

Q5: Can I use this for vertical launches?
A: Yes, for vertical launches (90°), the range will be 0 and the height follows standard free-fall equations.