How to Calculate Boat Velocity Relative to Shore in River Flow?

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When a boat traveling at 10 km/hr in still water moves upstream against a river current of 10 km/hr, its velocity relative to the shore is 0 km/hr, effectively canceling out the current. Conversely, when the boat travels downstream with the current, its velocity relative to the shore is 20 km/hr, combining both speeds. To analyze the boat's movement when oriented at right angles to the current, vector components and vector addition principles must be applied to determine the resultant direction and speed. The discussion emphasizes understanding the process of vector addition rather than focusing solely on numerical answers. This knowledge is crucial for solving related problems in the context of river flow and boat velocity.
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Consider a boat that travels at 10 km/hr in still (non-moving) water. If the boat travels in a river that flows at a rate of 10 km/hr, what will be its velocity relative to the shore when it heads directly upstream (against the current)? What happens when it heads downstream (with the flow)? Explain




Suppose the boat is oriented at right angles to the water flow and begins moving. Using vector components and vector addition rules, how would you go about finding the direction in which the boat will move relative to the shore? I am interested in the process, not the numerical answer.


I have not been able to purchase the text needed for the class yet and I have an online quiz, so I am not able to figure out how to do these problems can anyone help?
 
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