➡️ Resultant Velocity Calculator
Calculate resultant velocity
Velocity 1
Velocity 2
How to Use This Calculator
Enter Velocity 1 Components
Input the X and Y components of the first velocity vector, measured in meters per second (m/s). These represent the velocity in the horizontal (x) and vertical (y) directions.
Enter Velocity 2 Components
Input the X and Y components of the second velocity vector, also in m/s. These represent another velocity that you want to combine with the first velocity.
Click Calculate
Press the "Calculate" button to compute the resultant velocity by adding the two velocity vectors component-wise, then calculating the magnitude and direction.
Review Results
The calculator displays the resultant velocity magnitude, direction (angle), and the X and Y components of the combined velocity vector.
Formula
v_resultant_x = v1_x + v2_x
v_resultant_y = v1_y + v2_y
|v_resultant| = √(v_resultant_x² + v_resultant_y²)
θ = arctan(v_resultant_y / v_resultant_x)
Where:
v_resultant = Resultant velocity vector
v1_x, v1_y = Components of velocity 1 (m/s)
v2_x, v2_y = Components of velocity 2 (m/s)
|v_resultant| = Magnitude of resultant velocity (m/s)
θ = Direction angle (degrees from x-axis)
Example 1: Perpendicular velocities
Given: v1 = (5, 0) m/s, v2 = (0, 3) m/s
Step 1: Add components
v_resultant_x = 5 + 0 = 5 m/s
v_resultant_y = 0 + 3 = 3 m/s
Step 2: Calculate magnitude
|v| = √(5² + 3²) = √(25 + 9) = √34 = 5.83 m/s
Step 3: Calculate angle
θ = arctan(3/5) = 30.96°
Example 2: Opposite directions
Given: v1 = (10, 0) m/s, v2 = (-5, 0) m/s
v_resultant_x = 10 + (-5) = 5 m/s
v_resultant_y = 0 + 0 = 0 m/s
|v| = √(5² + 0²) = 5 m/s
θ = 0° (moving along positive x-axis)
Example 3: General case
Given: v1 = (3, 4) m/s, v2 = (2, 1) m/s
v_resultant = (3+2, 4+1) = (5, 5) m/s
|v| = √(5² + 5²) = √50 = 7.07 m/s
θ = arctan(5/5) = arctan(1) = 45°
About Resultant Velocity Calculator
The Resultant Velocity Calculator is a fundamental physics tool for calculating the combined velocity from two velocity vectors. When an object has multiple velocities acting simultaneously (such as a boat moving on water with a current, or an airplane flying with wind), the resultant velocity is the vector sum of all individual velocities. This calculator adds two velocity vectors component-wise and computes the magnitude (speed) and direction (angle) of the resulting velocity vector. Understanding resultant velocity is essential in physics, engineering, navigation, and any situation involving relative motion.
When to Use This Calculator
- Physics Problems: Calculate combined velocities when multiple velocities act simultaneously
- Navigation: Determine actual velocity of boats or aircraft with wind or current effects
- Relative Motion: Analyze motion when objects move relative to moving reference frames
- Vector Addition: Practice and understand vector addition in physics
- Engineering Applications: Calculate velocities in mechanical systems with multiple motion components
- Educational Purposes: Learn about vector addition and velocity composition
Why Use Our Calculator?
- ✅ Vector Addition: Automatically adds velocity vectors component-wise
- ✅ Complete Results: Provides magnitude, direction, and components of resultant velocity
- ✅ Accurate Calculations: Uses precise vector mathematics and trigonometry
- ✅ Educational Value: Shows formulas and step-by-step calculations
- ✅ Visual Understanding: Displays components to help visualize vector addition
- ✅ Real-World Applications: Essential for navigation and relative motion problems
Common Applications
Navigation: Calculate the actual velocity of a boat moving on water with a current, or an airplane flying with wind. The boat's velocity relative to water plus the water's velocity relative to ground equals the boat's velocity relative to ground.
Physics Problems: Solve problems involving relative motion, such as objects moving on moving platforms, or projectiles launched from moving vehicles.
Engineering: Analyze velocities in mechanical systems where multiple motion components combine, such as conveyor belts on moving platforms or rotating objects with translational motion.
Physics Education: Help students understand vector addition, demonstrating how velocities combine to produce a resultant velocity with both magnitude and direction.
Tips for Best Results
- Use Consistent Units: Ensure all velocity components are in the same units (typically m/s)
- Sign Matters: Use positive/negative values to indicate direction (positive = right/up, negative = left/down)
- Component Addition: Add X components together and Y components together separately
- Magnitude is Always Positive: The resultant speed is always positive, but direction can vary
- Right Triangle: Resultant magnitude uses Pythagorean theorem: |v| = √(v_x² + v_y²)
Frequently Asked Questions
What is resultant velocity?
Resultant velocity is the combined velocity from adding two or more velocity vectors. When velocities act simultaneously (like a boat's velocity plus water current velocity), the resultant is the vector sum. It represents the actual velocity of the object relative to a fixed reference frame.
How do you add velocity vectors?
Velocity vectors are added component-wise: add the X components together and the Y components together. The resultant velocity components are v_resultant_x = v1_x + v2_x and v_resultant_y = v1_y + v2_y. Then find the magnitude using the Pythagorean theorem.
What's the difference between speed and velocity?
Speed is a scalar (magnitude only), while velocity is a vector (magnitude and direction). The calculator shows the magnitude (speed) of the resultant velocity, but also provides the direction (angle) and components, giving you the complete velocity vector.
Can velocities cancel out?
Yes! If two velocities are equal in magnitude but opposite in direction, they cancel out. For example, v1 = (10, 0) and v2 = (-10, 0) gives v_resultant = (0, 0), meaning the object is stationary (zero resultant velocity).
What if velocities are perpendicular?
When velocities are perpendicular (like v1 = (5, 0) and v2 = (0, 3)), the resultant magnitude is simply the hypotenuse of the right triangle: |v| = √(5² + 3²) = 5.83 m/s. The angle is arctan(3/5) = 30.96°.
How is this used in real-world scenarios?
Common examples: (1) A boat moving north at 5 m/s on water flowing east at 3 m/s - the boat's actual path is northeast. (2) An airplane flying east at 200 m/s with wind blowing north at 20 m/s - the plane's ground track is slightly northeast. (3) A person walking on a moving train - their velocity relative to ground is their walking velocity plus the train's velocity.