How to Calculate the Correct Angle and Time to Cross a River in a Powerboat?

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To cross a 310-meter-wide river with a current speed of 1.6 m/s, the explorer must calculate the correct angle to point the boat, which travels at 4.4 m/s relative to the water. The boat needs to be aimed upstream to counteract the river's flow and reach a clearing on the north bank, located 11 meters upstream. The discussion raises questions about whether the 4.4 m/s speed refers to magnitude or a specific component of velocity. Understanding the distinction between speed and velocity is crucial for accurate calculations. Ultimately, determining the angle and time to cross requires applying principles of vector resolution and relative motion.
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A 310-m-wide river has a uniform flow speed of 1.6 m/s through a jungle and toward the east. An explorer wishes to leave a small clearing on the south bank and cross the river in a powerboat that moves at a constant speed of 4.4 m/s with respect to the water. There is a clearing on the north bank 11 m upstream from a point directly opposite the clearing on the south bank. (a) At what angle, measured relative to the direction of flow of the river, must the boat be pointed in order to travel in a straight line and land in the clearing on the north bank? (b) How long will the boat take to cross the river and land in the clearing?


I don't know whether the 4.4 m/s is a magnitude or the y-component.
 
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chaudown said:
An explorer wishes to leave a small clearing on the south bank and cross the river in a powerboat that moves at a constant speed of 4.4 m/s with respect to the water.

I don't know whether the 4.4 m/s is a magnitude or the y-component.
What is speed in relation to velocity?
 
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