Relative Motion · Interactive

Crossing a River

The boat's engine drives it through the water, but the water itself is flowing. What the riverbank sees is the sum of the two: the boat's velocity relative to the water plus the water's velocity relative to the ground. Steer the boat and watch how the current reshapes its path.

vboat / water vwater / ground vboat / ground Top-down view · current flows →

Setup

Heading θ from straight across0°
Boat speed v_b3.0 m/s
Current speed v_r1.5 m/s
Drifting downstream
Outcome
6.7 s
time to cross
10.0 m
drift downstream
3.4 m/s
ground speed
30°
θ for zero drift

Aim for the dot: the hollow marker on the far bank is directly opposite the start. Angle the boat upstream until the amber resultant points straight at it — that happens when sin θ = v_r / v_b, and the drift falls to zero.