Mechanics question (vector descriptions of two birds' flight paths)

In summary, the conversation is discussing the task of finding the position vector and speed of bird B relative to bird A after 4 seconds. The speaker mentions being able to find the position vector but being unsure of how to find p and the speed of bird B. They mention that bird B is south west of bird A, which can be interpreted as being at 45 degrees west of south.
  • #1
trew
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Homework Statement
as below
Relevant Equations
as below
2019ialvector.JPG

Part (a) was fine.

For part (b), I started off with finding the position vector of bird A and bird B after 4 seconds, and this was:

Position vector of A after 4 seconds: -4i + 11j

Position vector of B after 4 seconds: (-8 + 4p)i + (9+8p)j

But after this I'm lost.

Usually I'd have some idea but honestly right now I have no idea. What am I missing here?
 
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  • #2
The statement "bird B is south west of bird A" can be interpreted to mean that the position vector of bird B relative to bird A is at 45o West of South. If you can find an expression for that vector at t = 4 s, you should be able to find p and hence the speed of bird B.
 
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FAQ: Mechanics question (vector descriptions of two birds' flight paths)

1. What is the difference between a scalar and a vector quantity in mechanics?

A scalar quantity only has magnitude, while a vector quantity has both magnitude and direction. In the context of two birds' flight paths, the scalar quantity would be the distance traveled and the vector quantity would be the displacement, which takes into account the magnitude and direction of the birds' movements.

2. How do you calculate the net displacement of two birds with different flight paths?

To calculate the net displacement, you need to find the vector sum of the two birds' displacement vectors. This can be done by adding the x-components and y-components of each vector separately, using vector addition. The resulting vector will represent the net displacement of the two birds.

3. Can the two birds have the same displacement but different velocities?

Yes, it is possible for two birds to have the same displacement but different velocities. Displacement only takes into account the overall change in position, while velocity also includes the direction and speed of the movement. Therefore, the birds could have traveled the same distance but at different speeds or in different directions.

4. How do you represent the flight paths of the two birds using vectors?

The flight paths of the two birds can be represented using position vectors. These vectors would have their initial point at the starting position of each bird, and their terminal point at the corresponding final position. The direction and magnitude of the vectors would represent the direction and distance traveled by each bird.

5. Can the two birds collide if their flight paths are represented by intersecting vectors?

Yes, if the two birds' flight paths are represented by intersecting vectors, it is possible for them to collide. This would occur if their displacement vectors intersect at some point, indicating that they are both at the same position at the same time. However, it is important to note that the intersection of their vectors alone does not necessarily guarantee a collision, as the birds could still be at different heights or have different trajectories.

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