You want to cross a straight section of a river that has a uniform current of 5.

Question

You want to cross a straight section of a river that has a uniform current of 5.20 m/s and is 140. m wide. Your motorboat has an engine that can generate a speed of 15.0 m/s for your boat. Assume that you reach top speed right away (that is, neglect the time it takes to accelerate the boat to top speed).


(a) In which direction should you aim your boat to achieve minimum crossing time? (0° = ? = 90° relative to the riverbank.)
? = °

(b) What is the minimum time to cross the river?


(c) What is the minimum speed of your boat that will still enable you to cross the river with a 90° angle relative to the riverbank?

Explanation / Answer

a.) To achieve minimum crossing time, you should aim at an angle of 90 degrees (head straight across) so that all of your velocity is going into heading across the river instead of having some of it used to fight the current. b.) The minimum time to cross is: d = V * t 140m = 15m/s * t t = 9.33 seconds c.) The minimum speed you could cross the river with a 90 degree angle relative to the riverbank would be 5.2 m/s. This is because you need enough speed to cancel out the river's current (which is 5.2 m/s) in order to maintain a 90 degree angle.

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