If a = 0.5 mi and v₀ = 9 mi/h as in Example 4, what must the swimmer’s speed v_S be in order that he drifts only 1 mile downstream as he crosses the river?

Example 4

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Example 4 River crossing Suppose that the river is 1 mile wide and that its midstream velocity is vo = 9 mi/h. If the swimmer's velocity is v5 = 3 mi/h, then Eq. (19) takes the form Integration yields dy dx Then = 3(1-4x²). y(x) = (3-12x²) dx = 3x - 4x³ + +C for the swimmer's trajectory. The initial condition y(-) = 0 yields C = 1, so y(x) = 3x - 4x³ + 1. 3 y ( ) = 3 (1)-4 ( 4 ) ³ + 1 so the swimmer drifts 2 miles downstream while he swims 1 mile across the river. +1=2,