Maxi Calculator

Resultant Velocity Calculator

Calculate the resultant velocity from two velocity vectors

Resultant Velocity Calculator

Enter the first velocity in m/s

Enter the first angle in degrees (0-360)

Enter the second velocity in m/s

Enter the second angle in degrees (0-360)

Table of Contents
What is Resultant Velocity?

Resultant velocity is the single velocity vector that represents the combined effect of two or more velocity vectors. It is found by vector addition and has both:

  • Magnitude (speed)
  • Direction (angle)

Understanding resultant velocity is crucial in physics and engineering for analyzing motion, navigation, and force interactions.

Vector Addition Method

Graphical Method

Vectors can be added graphically by placing them tip-to-tail and drawing the resultant from the start of the first vector to the end of the last vector.

Component Method

For mathematical precision, we use the component method:

  • Break each vector into x and y components
  • Add the x components together
  • Add the y components together
  • Calculate the magnitude and direction of the resultant vector
Vector Components

Component Equations

  • x-component = v × cos(θ)
  • y-component = v × sin(θ)
  • Resultant magnitude = √(x² + y²)
  • Resultant angle = tan⁻¹(y/x)

Important Notes

  • Angles are measured counterclockwise from the positive x-axis
  • The resultant angle must be adjusted based on the quadrant
  • Components can be positive or negative depending on direction
Examples

Example 1: Perpendicular Velocities

A boat travels east at 3 m/s while a current pushes it north at 4 m/s:

  • Resultant velocity = √(3² + 4²) = 5 m/s
  • Direction = tan⁻¹(4/3) = 53.1°

Example 2: Arbitrary Angles

Two velocities: 10 m/s at 30° and 15 m/s at 120°:

  • x-components: 10cos(30°) + 15cos(120°) = 8.66 - 7.5 = 1.16 m/s
  • y-components: 10sin(30°) + 15sin(120°) = 5 + 13 = 18 m/s
  • Resultant velocity = √(1.16² + 18²) = 18.04 m/s
  • Direction = 86.3°
Frequently Asked Questions

Why do we need vector addition for velocities?

Vector addition is necessary because velocity has both magnitude and direction. Simple scalar addition would not account for the directional nature of motion.

What is the difference between speed and velocity?

Speed is a scalar quantity (magnitude only), while velocity is a vector quantity (magnitude and direction). The resultant velocity calculator considers both aspects.

Can the resultant velocity be less than either component?

Yes, if the velocity vectors are pointing in opposing directions, the resultant velocity can be smaller than either of the component velocities.