Direction of Final Velocity of Vehicles after Collision Calculator

Formula Used:

\[ \theta = \tan^{-1}\left(\frac{V_{fy}}{V_{fx}}\right) \]

Direction of Final Velocity (θ):

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1. What is the Direction of Final Velocity Formula?

The direction of final velocity formula calculates the angle of trajectory for a vehicle after a collision using the inverse tangent of the ratio between the y-component and x-component of the final velocity.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \theta = \tan^{-1}\left(\frac{V_{fy}}{V_{fx}}\right) \]

Where:

\( \theta \) — Direction of Final Velocity (degrees)
\( V_{fy} \) — Final Velocity after Collision in Y-Direction (m/s)
\( V_{fx} \) — Final Velocity after Collision in X-Direction (m/s)

Explanation: The formula calculates the angle using trigonometric principles, specifically the inverse tangent function applied to the ratio of vertical and horizontal velocity components.

3. Importance of Direction Calculation

Details: Calculating the direction of final velocity is crucial in accident reconstruction, vehicle dynamics analysis, and understanding post-collision trajectories for safety assessments and legal investigations.

4. Using the Calculator

Tips: Enter both velocity components in meters per second. The x-direction velocity cannot be zero as division by zero is undefined. Results are provided in degrees.

5. Frequently Asked Questions (FAQ)

Q1: Why use inverse tangent for direction calculation?
A: Inverse tangent (atan) is used because it directly relates the ratio of opposite side (Vfy) to adjacent side (Vfx) in a right triangle to the angle between them.

Q2: What if Vfx is zero?
A: If Vfx is zero, the direction becomes undefined (division by zero). This represents purely vertical motion where the angle would be 90° or 270° depending on Vfy's sign.

Q3: How are negative velocity components handled?
A: Negative components are handled correctly by the atan function, producing angles in the appropriate quadrant based on the signs of both components.

Q4: What's the range of possible angle values?
A: The atan function typically returns values between -90° and 90°, but quadrant adjustments are made based on input signs to provide the correct direction.

Q5: Can this be used for 3D collisions?
A: This formula calculates direction in 2D space. For 3D collisions, additional calculations involving the z-component would be required.