calculate_projectile_motion
Calculate projectile motion trajectory, including maximum height, range, time of flight, and sample points for plotting.
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 |