🚣 Relative Velocity — River Crossing

Relative Velocity Simulator: River Crossing & Boat Drift

This relative velocity simulator drops a boat into a flowing river so you can see velocities add as vectors: the boat's motion over the ground is its velocity through the water plus the river's current. Point straight across and the current sweeps the boat downstream along a slanted path; aim upstream and the boat's sideways component fights the current. Hit the exact angle where v_boat·sinφ = v_current and the drift cancels, landing you straight across — or ask the lab to auto-aim it. Live arrows show the boat velocity (blue), the current (green), and their resultant ground velocity (orange), while a card reports the across speed, net downstream speed, crossing time, and final drift. A key insight emerges: heading straight across is always the fastest crossing even though it drifts, because only the across-component shortens the trip. Predict where the boat lands before you launch.

What you can do in this simulation

• Steer a boat across a river and watch the current add a downstream drift to its path
• Live boat, current, and resultant ground-velocity arrows show v_ground = v_boat + v_current
• Aim upstream (or auto-aim) so v_boat·sinφ = v_current and land straight across the start point
• A card tracks across speed, net downstream speed, crossing time, and drift at the far bank
• Predict mode: call upstream / straight / downstream before launching; see why straight-across is the fastest crossing

Concepts covered

relative velocity · river crossing problem · vector addition · reference frames · crosswind and current · resultant velocity · drift

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