# A calculus problem by Rocco Dalto

Calculus Level pending

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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