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River Crossing Relative Velocity

Run the River Crossing MicroSim Fullscreen Edit the River Crossing MicroSim Using the p5.js Editor

Description

This MicroSim demonstrates relative velocity through a classic physics scenario: crossing a river with a current. A swimmer aims to reach a point directly across the river, but the current carries them downstream. The simulation shows how vector addition determines the actual path.

Key Concepts

  • Relative Velocity: The swimmer's velocity relative to water combines with the water's velocity relative to ground
  • Vector Addition: \(\vec{v}_{result} = \vec{v}_{swimmer} + \vec{v}_{current}\)
  • Crossing Time: Depends only on swimmer speed and river width: \(t = \frac{d}{v_{swim}}\)
  • Downstream Drift: \(x_{drift} = v_{current} \times t\)
  • Aiming Upstream: To travel straight across, aim at angle \(\theta = \arcsin(v_{current}/v_{swim})\)

How to Use

  1. Adjust Swim speed (swimmer's speed relative to water)
  2. Adjust Current speed (river flow rate)
  3. Click Swim to start the crossing
  4. Observe the three velocity vectors:
    • Blue: Swimmer velocity (relative to water)
    • Red: Current velocity
    • Purple: Resultant velocity (actual motion)
  5. Enable Aim Upstream to see how the swimmer can compensate for current

Learning Objectives

After using this MicroSim, students should be able to:

  1. Apply vector addition to find resultant velocity
  2. Calculate downstream drift from current speed and crossing time
  3. Determine the angle needed to travel straight across
  4. Explain why crossing time depends only on the perpendicular velocity component