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🌊 River Crossing Problem

Relative Velocity NEET · JEE · KCET 2D Motion
🏊 Swimmer 📈 Actual Path 🌊 River Flow → 🏁 Start → Finish
v_sy = v_s·cosθ | v_sx = v_s·sinθ | v_net_x = v_sx + v_r
Time = w / v_sy | Drift = v_net_x × Time
Time to cross
0.00
s
Downstream Drift
0.0
m
Resultant Speed
0.00
m/s
v_sx (horizontal)
0.00
m/s
v_s = 2.0 m/s at 0° | v_r = 1.5 m/s →
v_net = v_s + v_r = (0.00, 2.00) m/s

🎯 Optimal Angle for Zero Drift

θ = 0°
(swim upstream to cancel river flow)

🔍 What to Observe

  • At θ = 0°, time = w/v_s (minimum time)
  • Drift increases with river speed (v_r)
  • To reach directly opposite, swim upstream at θ = sin⁻¹(v_r/v_s)
  • If v_s > v_r, zero drift is possible
  • If v_s ≤ v_r, zero drift is impossible
Ready
Position: (0, 0)