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 — the crossing time, which depends only on the part of the velocity pointing across the river.
Como usar esta simulação
- 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
O que observar
- 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
A física por trás
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 θ with sin θ = v_c/v_b, which cancels the drift but cuts the across-river component to v_b cos θ and so lengthens the crossing.