1. What is Resultant Velocity?

Resultant velocity is the vector sum of two or more velocities. It represents the combined effect of multiple velocity vectors acting simultaneously, taking into account both their magnitudes and directions.

2. How Does the Calculator Work?

The calculator uses the resultant velocity formula:

Where:

• \( v_1 \) — First velocity magnitude (m/s)
• \( v_2 \) — Second velocity magnitude (m/s)
• \( \theta \) — Angle between the two velocity vectors (degrees)

Explanation: This formula calculates the magnitude of the resultant vector when two vectors are added using the law of cosines.

3. Applications of Resultant Velocity

Details: Resultant velocity calculations are essential in physics, engineering, navigation, and sports science. They help determine the combined effect of multiple motions, such as wind affecting aircraft speed or currents affecting boat navigation.

4. Using the Calculator

Tips: Enter both velocities in meters per second (m/s) and the angle between them in degrees (0-360°). All values must be non-negative.

5. Frequently Asked Questions (FAQ)

Q1: What happens when θ = 0°?
A: When the angle is 0°, the vectors are parallel and in the same direction, resulting in maximum resultant velocity (v₁ + v₂).

Q2: What happens when θ = 180°?
A: When the angle is 180°, the vectors are in opposite directions, resulting in minimum resultant velocity (|v₁ - v₂|).

Q3: What happens when θ = 90°?
A: When the angle is 90°, the vectors are perpendicular, and the resultant is calculated using the Pythagorean theorem (√(v₁² + v₂²)).

Q4: Can this formula be used for more than two vectors?
A: This specific formula is for two vectors. For more vectors, you would need to add them sequentially or use component methods.

Q5: Does the formula work for any angle value?
A: Yes, the formula works for any angle between 0° and 360°, with the cosine function properly handling the directionality.