1. What is Relative Velocity?

Relative velocity is the velocity of an object or observer B in the rest frame of another object or observer A. It is calculated using vector components to determine the magnitude of the resultant velocity vector.

2. How Does the Calculator Work?

The calculator uses the relative velocity formula:

Where:

• \( v_x \) — X-component of velocity (m/s)
• \( v_y \) — Y-component of velocity (m/s)
• \( v_{rel} \) — Resultant relative velocity (m/s)

Explanation: This formula calculates the magnitude of the resultant vector from its perpendicular components using the Pythagorean theorem.

3. Importance of Relative Velocity Calculation

Details: Relative velocity calculations are essential in physics, engineering, navigation, and many real-world applications such as aircraft navigation, projectile motion analysis, and collision avoidance systems.

4. Using the Calculator

Tips: Enter both velocity components in m/s. The calculator will compute the magnitude of the resultant velocity vector. Both values can be positive or negative, representing direction.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator handle 3D velocity vectors?
A: This calculator is designed for 2D vectors. For 3D vectors, the formula would be \( v_{rel} = \sqrt{v_x^2 + v_y^2 + v_z^2} \).

Q2: What if my velocity components are negative?
A: Negative values are acceptable as they represent direction. The squaring operation in the formula will make them positive before the square root is applied.

Q3: How accurate is this calculation?
A: The calculation is mathematically exact for the given components. The result is rounded to 4 decimal places for display purposes.

Q4: Can I use this for non-orthogonal components?
A: No, this formula assumes the components are perpendicular (orthogonal). For non-orthogonal components, vector addition using the law of cosines would be needed.

Q5: What units should I use?
A: The calculator expects inputs in m/s, but any consistent velocity units can be used as long as both components are in the same units.