Physics — Two-Dimensional Relative Motion · River-crossing vector simulation

River Crossing: Relative Motion Simulation

Investigate how the boat’s velocity through water combines with river current to determine its path and drift.

Landscape activity · use fullscreen on a phone for larger controls

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📝 Description

River Crossing is a relative motion simulation that helps students understand boat velocity, river flow, resultant motion, and crossing time. It makes vector addition and two-dimensional motion easier to visualize for classroom and self-study use.

📋 Instructions

Adjust the boat and river settings, start the simulation, and observe the resultant path. Compare directions, speed, and crossing behavior.

🎓 Learning Guide: River Crossing: Relative Motion Simulation

Learning focus: Investigate how the boat’s velocity through water combines with river current to determine its path and drift.

Physics — Two-Dimensional Relative Motion River-crossing vector simulation

Learning objectives

Distinguish velocity relative to water from velocity relative to ground.
Predict downstream drift and crossing time using velocity components.
Describe the idea of heading upstream to reduce drift.

Concepts and principles

Ground velocity is the vector sum of boat-through-water velocity and river-current velocity.
Across-river crossing time equals river width divided by the across-stream component of ground velocity, where nonzero.
Zero drift is possible only if the upstream boat-velocity component can cancel the current; otherwise minimum drift is nonzero.

Examples and worked solutions

A boat heads straight across a 100 m river at 5 m/s relative to water while current flows at 2 m/s. Find crossing time and drift.: Worked solution: Crossing time=100/5=20 s. Downstream drift=2×20=40 m, assuming steady current and speed.

Try this investigation

Observe the river-current and player-velocity vectors before changing a slider.
Change one displayed velocity at a time and compare trajectory or trace.
Where the game offers a minimum-drift challenge, predict the heading needed and check the result.

Expected observations and explanations

A stronger current usually increases downstream drift for the same crossing time.
Steering upstream can reduce drift but may also reduce the across-stream velocity component.

Assessment questions and answers

Why is the actual boat path not straight across in that example?: Answer: The river adds a downstream component to the boat’s ground velocity.
Can every current be cancelled by steering upstream?: Answer: No. If the current exceeds the available upstream component of the boat’s velocity, zero drift is impossible.