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Relative Velocity Problem Solver

Run the Relative Velocity Solver Fullscreen

Description

This MicroSim helps you visualize and solve relative velocity problems involving two moving objects. Set the speed and direction of objects A and B, then see how to calculate the velocity of A relative to B using vector subtraction.

Key Concepts

  • Relative Velocity Formula: \(\vec{v}_{AB} = \vec{v}_A - \vec{v}_B\)
  • Component Method:
    • \(v_{ABx} = v_{Ax} - v_{Bx}\)
    • \(v_{ABy} = v_{Ay} - v_{By}\)
  • Magnitude: \(|\vec{v}_{AB}| = \sqrt{v_{ABx}^2 + v_{ABy}^2}\)
  • Direction: \(\theta = \tan^{-1}(v_{ABy}/v_{ABx})\)

How to Use

  1. Select a Preset scenario or keep Custom
  2. Adjust A speed and A angle for object A's velocity
  3. Adjust B speed and B angle for object B's velocity
  4. View the calculated relative velocity (purple dashed vector)
  5. Click Animate to see both objects move
  6. Enable View from B to see the world from B's reference frame
  7. Enable Components to see x and y components

Preset Scenarios

  • Custom: Set your own values
  • Chase: Both objects moving in same direction
  • Head-on: Objects approaching each other
  • Perpendicular: Objects moving at right angles

Learning Objectives

After using this MicroSim, students should be able to:

  1. Calculate relative velocity using vector subtraction
  2. Break velocities into components and subtract them
  3. Find magnitude and direction of the relative velocity vector
  4. Understand how motion appears from different reference frames
  5. Apply relative velocity to real-world scenarios (boats, planes, etc.)