Ballistic Angle of Velocity Calculator

Y Velocity (\( v_y \)):

X Velocity (\( v_x \)):

Ballistic Angle (\( \alpha \)) in degrees (°):

Ballistic Angle (\( \alpha \)) in radians (rad):

Ballistic Angle (\( \alpha \)) in gradians (grad):

1. What is the Ballistic Angle of Velocity Calculator?

Definition: This calculator determines the ballistic angle of velocity (\( \alpha \)) based on the velocity components in the Y direction (\( v_y \)) and X direction (\( v_x \)).

Purpose: It assists physicists and engineers in analyzing the trajectory angle of projectiles or objects in motion.

2. How Does the Calculator Work?

The calculator uses the relationship:

\[ \alpha = \arctan\left(\frac{v_y}{v_x}\right) \]

Where:

\( \alpha \) — Ballistic angle of velocity (in degrees, radians, or gradians)
\( v_y \) — Velocity component in the Y direction
\( v_x \) — Velocity component in the X direction

Explanation: Enter the velocity components in the chosen units, and the calculator computes the angle using the arctangent function. Results use scientific notation (5 decimal places) if the angle in degrees is greater than 1000 or less than 0.00001, otherwise 2 decimal places. The image does not provide sample inputs or outputs, so default values are used for testing.

3. Importance of Ballistic Angle

Details: The ballistic angle is crucial for understanding the trajectory of projectiles, used in ballistics, aerospace, and sports science.

4. Using the Calculator

Tips: Enter values for Y velocity and X velocity (ensure \( v_x \neq 0 \)), then click "Calculate." Results show the angle in degrees, radians, and gradians (scientific notation with 5 decimal places if > 1000 or < 0.00001 degrees, otherwise 2 decimal places).

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