Here's a breakdown:
1. One-Dimensional Motion:
* Same direction: If two velocities, v1 and v2, act in the same direction, the resultant velocity (vr) is simply the sum of the individual velocities:
* vr = v1 + v2
* Opposite directions: If two velocities act in opposite directions, the resultant velocity is the difference between the two velocities:
* vr = v1 - v2 (where the larger velocity is taken as positive)
2. Two-Dimensional Motion:
* When velocities are at an angle: This is where things get more complex, requiring vector addition. We use the Pythagorean theorem and trigonometry.
* Resultant velocity magnitude:
* vr = √(v1² + v2² + 2v1v2cosθ)
* where θ is the angle between the two velocity vectors.
* Resultant velocity direction:
* tan(α) = (v2sinθ) / (v1 + v2cosθ)
* where α is the angle of the resultant velocity vector relative to the direction of v1.
Meaning:
The resultant velocity is the overall velocity of an object that is moving with multiple velocities simultaneously. It represents the net effect of all the individual velocities acting on the object.
Examples:
* A boat traveling across a river: The boat has its own velocity, and the river current has its own velocity. The resultant velocity of the boat is the combination of these two velocities, determining the boat's actual path.
* A projectile launched at an angle: The initial velocity of the projectile has a horizontal and vertical component. The resultant velocity of the projectile changes throughout its flight due to the combined effects of gravity and the initial velocity.
Key points to remember:
* Velocity is a vector quantity, meaning it has both magnitude (speed) and direction.
* The resultant velocity is the vector sum of all individual velocities.
* The direction of the resultant velocity is determined by the angle between the individual velocities.
* The magnitude of the resultant velocity is influenced by the magnitudes of the individual velocities and the angle between them.
