calculate_projectile_motion
Calculate projectile motion trajectory including maximum height, range, and flight time for ballistics, sports analysis, or educational demonstrations.
Instructions
Calculate projectile motion trajectory using kinematic equations.
Computes the complete trajectory of a projectile launched at an angle,
including maximum height, range, time of flight, and sample trajectory points.
Perfect for ballistics, sports analysis, or educational demonstrations.
Args:
initial_velocity: Initial velocity in meters per second (m/s). Must be positive.
angle_degrees: Launch angle in degrees from horizontal (0-90).
0° = horizontal, 45° = maximum range, 90° = straight up
initial_height: Initial height above ground in meters. Default 0.0 (ground level).
gravity: Gravitational acceleration in m/s². Default 9.81 (Earth surface).
Use 1.62 for Moon, 3.71 for Mars, etc.
Returns:
ProjectileMotionResponse containing:
- max_height: Maximum height reached (meters)
- range: Horizontal distance traveled (meters)
- time_of_flight: Total time in air (seconds)
- trajectory_points: List of [x, y] sample points for plotting
Tips for LLMs:
- 45° gives maximum range on flat ground (no air resistance)
- For R3F visualization: convert trajectory_points to 3D by adding z=0
- trajectory_points are evenly spaced in time (50 samples)
- Air resistance is NOT modeled - this is ideal ballistic motion
- Use for: cannon balls, baseballs, basketball shots, water fountains
Example:
# Calculate trajectory of a cannonball fired at 50 m/s at 30°
result = await calculate_projectile_motion(
initial_velocity=50.0,
angle_degrees=30.0,
initial_height=2.0
)
print(f"Range: {result.range:.1f}m, Max height: {result.max_height:.1f}m")Input Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| initial_velocity | Yes | ||
| angle_degrees | Yes | ||
| initial_height | No | ||
| gravity | No |