RIVER CROSSING
Straight across is fastest (but you drift); ferry upstream for zero drift at more time. And if the current wins, you can’t land straight across.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
A river a hundred metres wide, flowing steadily, and a boat that can only make so much speed through the water. You want the far bank. Two instincts fight: point straight at your target, or angle into the current to fight it.
Straight
Velocities add as vectors. Point straight across and your across-speed is exactly the boat speed — the current cannot touch it — so this crossing is the fastest there is. But the same current sweeps you downstream the whole way, and you land off-target.
Ferry
Aim upstream until sinφ = v_current/v_boat. Less speed remains across the river, so zero drift costs extra time.
Race
Race both boats: the straight-heading one arrives first downstream; the zero-drift ferry arrives opposite later.
Audit
Audited: the straight-heading time and drift are closed, and the minimum-time heading is straight across for any current. When the current matches or exceeds the boat, cancellation leaves zero or negative across-speed, so a zero-drift crossing is impossible.