BOAT & RIVER
v_boat5.0 m/s
v_river3.0 m/s
width100.0 m

AIM
heading0°
Keep trace

VECTOR VIEW

ACTIONS
VELOCITIES
v_boat
v_river
heading
v_actual

CROSSING
time
drift
path
t
t0.0 s

River Crossing

Point a boat straight across a flowing river and it will not reach the other side straight across. The water is moving, so it carries the boat downstream while you row. The boat faces one way but actually travels along a different line, and the angle between them is the whole point.

Controls

Set the boat's speed, the current's speed, and the width of the river. Aim with the heading slider, or drag the arrow heads directly on screen. Two ready-made cases: Shortest time points you straight across, Land opposite points you upstream by exactly the right amount to cancel the current. Switch the vector drawing between Parallelogram and Triangle. Keep trace holds up to eight crossings for comparison. Press Play to set off.

Variables and outputs

Three arrows drawn at the boat: its own motion through the water, the river's motion, and the two added together to give the path it actually takes. A faint line shows where you are heading before you set off. How far downstream you ended up is hidden until you land — the sim will not answer that question for you in advance. If the current is faster than the boat, Land opposite switches off and the sim says why.

Model assumptions

The current is the same everywhere across the width. The boat's speed through the water never changes. No wind, no depth.

Learning objective

You should be able to pick a heading for the fastest crossing, pick a different one to land straight across, and say why they are not the same.