t. Rather, an approximation to the current speed (measured

QUESTION:

The current speed \(V_{r}\)of a straight river such as that in Problem 28 is usually not a constant. Rather, an approximation to the current speed (measured in miles per hour) could be a function such as \(v_{r}(x)=30 x(1-x)\), 0 x y, whose values are small at the shores (in this case, \(\left.v_{r}(\mathrm{U})=\mathrm{U} \text { and } v_{r}(\mathrm{I})=\mathrm{U}\right)\) and largest in the middle of the river. Solve the DE in Problem 30 subject to \(v_{s}=2 \mathrm{mi} / \mathrm{h} \text { and } v_{r}(x)\) and \(v_{r}(x)\)is as given. When the swimmer makes it across the river, how far will he have to walk along the beach to reach the point (0, 0)?

Text Transcription:

v_r

v_{r}(x)=30 x(1-x)

v_r(0) = 0

v_r(1) = 0

y(1) = 0, where vs  2 mi/h

v_r(x)