A boat's speed relative to water is half the river-flow speed. To minimize downstream drift while crossing, the boat should move at what angle to the stream direction?
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A boat's speed relative to water is half the river-flow speed. To minimize downstream drift while crossing, the boat should move at what angle to the stream direction?

G1 Physics · Accepted Answer

Let river speed be 2u and boat speed relative to water be u. Let the boat direction make angle θ upstream from the normal to the river. Across-river component = u cosθ. Crossing time = d/(u cosθ). Downstream ground component = 2u-u sinθ. Drift: x = (2u-u sinθ)d/(u cosθ) = d(2secθ-tanθ). For minimum drift: d/dθ(2secθ-tanθ)=0 2secθtanθ-sec²θ=0 2sinθ=1 ⇒ θ=30° upstream from the normal. Therefore angle measured from stream direction is 90°+30°=120°.