Frames of reference/vectors question.

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In summary: 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.
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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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  • #2
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
 
  • #3
wait, why isn't the downstream component of the velocity parallel to shore?
 
  • #4
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
 

1. What is a frame of reference?

A frame of reference is a set of coordinate axes that are used to describe the position and motion of objects in space. It is a point of view or perspective from which measurements are taken.

2. What is the difference between an inertial and non-inertial frame of reference?

An inertial frame of reference is a frame in which Newton's first law of motion holds true. This means that an object at rest will remain at rest and an object in motion will continue to move at a constant velocity, unless acted upon by an external force. A non-inertial frame of reference is one in which this law does not hold true, usually due to the presence of acceleration or rotation.

3. How do vectors relate to frames of reference?

Vectors are quantities that have both magnitude and direction. In the context of frames of reference, vectors are used to describe the position, velocity, and acceleration of objects in a particular frame. They are also used to represent the change in position, velocity, and acceleration between different frames of reference.

4. Can two different frames of reference have the same vector representing an object's motion?

Yes, it is possible for two different frames of reference to have the same vector representing an object's motion. This is because the vector is a mathematical representation of the object's position, velocity, or acceleration, and it is independent of the frame of reference used to describe it. However, the values of the vector may differ in each frame depending on their relative positions and orientations.

5. How do frames of reference and vectors apply to real-life situations?

Frames of reference and vectors are used in many real-life situations, such as navigation, sports, and physics experiments. For example, in navigation, frames of reference are used to determine a ship's position and direction of travel. In sports, vectors are used to describe the motion of players and objects like balls. In physics experiments, frames of reference are used to measure and analyze the motion of objects in different scenarios.

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