River Vector Lab 3D

Combine boat velocity and river current to predict the landing point.

Ready

Drag to rotate view • Shift-drag to pan • wheel or pinch to zoom • tap boat to track

Quick start

1Choose example

2Set speeds

3Aim boat

4Launch

Blue shows the boat through water, teal shows the current, and orange shows the actual motion seen from shore.

Mode

Crossing examples

River & boat controls

Boat speed through water4.0 m/s

Current speed2.5 m/s

Aim upstream0°

River width80 m

Target dock0 m

What should I display?

boat through waterflow of wateractual shore viewtarget / error

Run & view

Simulation speed1×

Rotate 3D river0°

Camera height55°

Zoom1.00×

Crossing results

Elapsed time

0.00 s

Downstream drift

0.0 m

Actual shore speed

4.72 m/s

Miss distance

50.0 m

Predicted landing: 50.0 m downstream in 20.0 s.

The current changes downstream motion but does not change the across-river component.

Position-time evidence

across-river positiondownstream drift

Boat focus

No object selectedFree camera

Position: —Boat velocity: —Current: —Ground velocity: —

Teacher / investigation tools

Water directionTarget toleranceBoat massWind drift

Learning objectives

Add velocity vectors to predict a boat’s motion relative to the bank.
Separate across-river and downstream components.
Compare fastest crossing, shortest path, and target-dock strategies.
Calculate crossing time, drift, ground speed, and heading.
Distinguish motion relative to water from motion relative to land.

Three velocities

Boat relative to water points where the boat is aimed. Water relative to bank is the current. Their vector sum is the boat relative to bank.

Ground downstream component = current − boat speed × sine of upstream angle
Ground across component = boat speed × cosine of upstream angle
Crossing time = river width divided by across component
Drift = downstream component × crossing time

Common misconception: pointing the bow straight across does not usually produce a straight path across. The current changes the boat’s ground velocity throughout the trip.

Strategy trade-offs

Fastest crossing: aim perpendicular to the banks. This maximizes the across-river component but allows drift.
No-drift crossing: aim upstream enough to cancel the current. This works only if the boat is faster than the current.
Reach a target dock: choose a heading whose predicted drift equals the target’s downstream position.
Shortest ground path: cancel drift and travel straight across, but the crossing takes longer than the fastest strategy.

Guided investigations

1. What controls crossing time?

Select Aim straight across.
Double current speed without changing boat speed.
Compare crossing time and drift.
Explain why time stays nearly unchanged while drift increases.

2. Current stronger than boat

Select No-drift ferry.
Make current speed greater than boat speed.
Try every upstream heading.
Explain why a no-drift crossing becomes impossible.

3. Hit the rescue dock

Select Reach rescue dock.
Predict whether to aim upstream or downstream.
Adjust heading until target error is under 5 meters.
Use the vector triangle to justify your choice.

Deeper reasoning

The current affects only the downstream component in this model.
Increasing upstream angle reduces drift but also reduces across-river speed.
Two observers can measure different velocities for the same boat because velocity depends on the reference frame.
The route is straight when both velocity components stay constant, even though it may be diagonal.
Wind can add another downstream or upstream velocity component.

Questions for exploration

When does aiming upstream increase crossing time dramatically?
Can a boat move downstream while pointing upstream?
Why is the fastest route not always the shortest route?
How would a nonuniform current curve the route?
What changes if the current reverses direction?