Crossing the River
A ferry points its bow straight at the landing opposite and still arrives well downstream. Move the current up and down and one number refuses to move with it β the crossing time, which depends only on the part of the velocity pointing across the river.
How to use this simulation
- Press Bow straight across the river and vary the current to test the crossing time
- Press Aim upstream to cancel the drift and watch the crossing take longer
- Use Free heading to set any angle yourself and see both effects at once
- Load the worked example at 4.0 m/s against a 3.0 m/s current, or the exam-style swimmer
What to look for
- With the bow straight across, the crossing time does not change when the current does
- The downstream drift grows in direct proportion to the current speed
- Aiming upstream removes the drift entirely but always increases the crossing time
- A current faster than the boat makes landing directly opposite impossible
- The across-river and along-river motions never interfere with one another
The physics behind it
The boat's velocity relative to the bank is the vector sum of its velocity through the water and the current. Those components are independent, so the across-river component alone sets the crossing time, t = w/v_b when the bow points straight across, regardless of how fast the river runs. The current acts only along the bank and produces a drift x = v_c t downstream. To land directly opposite, the bow must be angled upstream by ΞΈ with sin ΞΈ = v_c/v_b, which cancels the drift but cuts the across-river component to v_b cos ΞΈ and so lengthens the crossing.