A boat has speed u relative to water in a river of speed v, with u > v. First it is aimed perpendicular to the bank; its crossing time is t₁. Next it is aimed upstream so that it reaches the point directly opposite; its crossing time is t₂. Then t₂/t₁ equals:
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Question

A boat has speed u relative to water in a river of speed v, with u > v. First it is aimed perpendicular to the bank; its crossing time is t₁. Next it is aimed upstream so that it reaches the point directly opposite; its crossing time is t₂. Then t₂/t₁ equals:

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G1 Physics · Accepted Answer

When aimed perpendicular to the bank, t₁ = d/u. For zero drift, cross-river speed is √(u² - v²), so t₂ = d/√(u² - v²). Hence t₂/t₁ = u/√(u² - v²) = 1/√(1 - v²/u²).

A boat has speed u relative to water in a river of speed v, with u &gt; v. First it is aimed perpendicular to the bank; its crossing time is t₁. Next it is aimed upstream so that it reaches the point directly opposite; its crossing time is t₂. Then t₂/t₁ equals:

A boat has speed u relative to water in a river of speed v, with u > v. First it is aimed perpendicular to the bank; its crossing time is t₁. Next it is aimed upstream so that it reaches the point directly opposite; its crossing time is t₂. Then t₂/t₁ equals: