Frames of reference/vectors question.

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Homework Help Overview

The discussion revolves around a problem involving frames of reference and vector components in the context of a boat navigating across a river with a current. The original poster is trying to determine the correct direction to steer the boat to reach the opposite bank directly, considering the river's flow.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster questions the reasoning behind the boat's speed being considered perpendicular to the shore and expresses confusion about the relationship between the boat's speed and the river's current. Other participants clarify the nature of the velocity components and their orientations.

Discussion Status

Participants are exploring the relationships between the boat's velocity, the river's current, and the resulting path. Clarifications have been offered regarding the orientation of the velocity components, but there is still some uncertainty about the original poster's understanding of these concepts.

Contextual Notes

The problem involves specific definitions of direction and speed, and assumptions about the boat's movement relative to the water and the shore are being examined. The discussion reflects the complexity of vector addition in a moving medium.

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The captain of a boat wants to travel directly across a river that flows due east with a speed of 1.48 m/s. He starts from the south bank of the river and wants to reach the north bank by traveling straight across the river. The boat has a speed of 5.64 m/s with respect to the water. What direction (in degrees) should the captain steer the boat? Note that 90° is east, 180° is south, 270° is west, and 360° is north.

In this problem, we were told to find the answer by taking 360 minus the inverse tangent of windspeed/boatspeed. I don't understand why the 'boatspeed with respect to the water' should be perpendicular to the shore. It seems to me that since the water is moving, the the 5.64m/s with respect to the water should be the hypotenuse of the triangle.

What's wrong with my thinking?
 
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seang said:
In this problem, we were told to find the answer by taking 360 minus the inverse tangent of windspeed/boatspeed. I don't understand why the 'boatspeed with respect to the water' should be perpendicular to the shore. It seems to me that since the water is moving, the the 5.64m/s with respect to the water should be the hypotenuse of the triangle.

What's wrong with my thinking?


The downstream component of the velocity is perpendicular to the shore because the river is flowing upstream, also perpendicular to the shore. To go straight across, the boat's velocity needs a downstream component to cancel the upstream 'push' the river would give it.

The hypotenuse of the triangle, in this case, would be the straight line velocity that would be followed by the boat in still water. The other leg is the vector sum of these two vectors.

Dot
 
wait, why isn't the downstream component of the velocity parallel to shore?
 
seang said:
wait, why isn't the downstream component of the velocity parallel to shore?

Yes. I'm sorry. The downstream component is parallel to the shore, perpendicular to the path actually traveled by the boat.

I think I need coffee.

Dot
 

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