The \( y \) axis and the line \( x = c \) are the banks of a river whose current has uniform speed \( \bf a \) in the negative \( y \) direction. \(\) A boat enters the river at the point \( (c,0) \) and heads directly toward the origin with speed \( \bf b \) relative to the water. \(\)

What are the conditions on \( \bf a \) and \( \bf b \) that will allow the boat to reach the opposite bank? Where will it land?

(1) \( \bf a < b \) and the boat will land at the origin \( (0,0) \). \(\)

(2) \( \bf a = b \) and the boat will land at \( (0,-\dfrac{c}{2}) \). \(\)

(3) \( \bf a > b \) and the boat will land at \( (0, -c) \) \(\)

(4) \( \bf a > b \) and the boat will never land. \(\)

(5) \( \bf a < b \) and the boat will never land. \(\)

(6) \( \bf a = b \) and the boat will never land.

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