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What Is Resultant Velocity?
Resultant velocity is the vector sum of two or more velocity vectors. When an object experiences motion from multiple sources simultaneously -- such as a boat crossing a river with a current, or an airplane flying through wind -- the actual velocity is the combination of all velocity components. The resultant velocity gives both the speed and direction of the combined motion.
Understanding resultant velocity is crucial in navigation, aviation, and any scenario involving relative motion. Pilots must account for wind velocity when plotting courses, and sailors must consider ocean currents when navigating between ports.
Resultant Velocity Formula
The formula uses the parallelogram law of vector addition. V is the resultant speed, V1 and V2 are the individual speeds, θ is the angle between the velocity vectors, and α is the direction of the resultant relative to V1.
Real-World Examples
- River crossing: A boat moves at 4 m/s across a river with a 3 m/s current perpendicular to its path. Resultant = √(16+9) = 5 m/s at 36.9 degrees downstream.
- Airplane in wind: A plane flying 250 km/h north with a 50 km/h crosswind from the west experiences a resultant of 255 km/h slightly east of north.
- Walking on a train: Walking at 2 m/s toward the front of a train moving at 30 m/s gives a ground speed of 32 m/s (same direction, 0-degree angle).
Conversion Table
| m/s | km/h | mph | knots |
|---|---|---|---|
| 1 | 3.6 | 2.237 | 1.944 |
| 5 | 18 | 11.18 | 9.72 |
| 10 | 36 | 22.37 | 19.44 |
| 50 | 180 | 111.85 | 97.2 |
Frequently Asked Questions
How do I find resultant velocity for perpendicular vectors?
When vectors are perpendicular (90 degrees), the formula simplifies to V = √(V1² + V2²), which is the Pythagorean theorem. The direction is arctan(V2/V1) from V1.
What is the difference between speed and velocity?
Speed is a scalar (magnitude only), while velocity is a vector (magnitude and direction). The resultant velocity includes both the resultant speed and the direction of the combined motion.
Can resultant velocity be less than either component?
Yes, when the angle between velocities exceeds 90 degrees, the resultant can be less than the larger component. At 180 degrees, the resultant equals the absolute difference of the two speeds.