Movement of 2 particles Described by vectors

[LinearMan]

We have 2 particles A and B - velocity vectors: v(A)=(2; 0), v(B)=(0; 3).
In time t=0 these particles were in r(A)=(-3; 0), r(B)=(0. -3) (both are also vectors)
Determine a vector of the reciprocal position of A and B (means the position of one relative to the other). Compute time and length of maximal reprochement of A and B.


We work with vectors, so for better understanding i tried to put them into x-y coordinate system but a came across a problem with direction of v(A) and v(B). So I can't imagine the whole situation. I think next step will be to write r(A), r(B) as r(t), t=time

 

[haruspex]

Determine a vector of the reciprocal position of A and B.

Does that mean the position of one relative to the other?
Please post your attempt at solution. (See forum rules.)

 

[LinearMan]

Does that mean the position of one relative to the other?
Please post your attempt at solution. (See forum rules.)

yes, it does

 

[haruspex]

I think next step will be to write r(A), r(B) as r(t), t=time[/b]

Yes, that would be a good move. For clarity, use r_A(t), r_B(t). Then you can also write down r_B-A(t)

 

[Nickie]

.

I would first clarify the coordinate system being used in this scenario. It seems that a standard Cartesian coordinate system is being used, with particle A initially positioned at (-3,0) and particle B at (0,-3). However, without knowing the direction of the velocity vectors, it is difficult to accurately visualize the movement of the particles.

Assuming that the velocity vectors are pointing in the positive x and y directions, respectively, we can determine the reciprocal position of A and B by subtracting the position vectors of B from A. This would give us a reciprocal position vector of (3,3), indicating that particle A is 3 units to the right and 3 units above particle B.

To compute the time and length of maximal approach, we would need to know the equations of motion for the particles. Without this information, it is not possible to accurately calculate these values. Additionally, the time and length of maximal approach would depend on the initial velocities and positions of the particles, as well as any external forces acting on them.

In conclusion, while we can determine the reciprocal position of the particles and understand their initial positions and velocities, further information is needed to accurately calculate the time and length of maximal approach. I would recommend gathering more data and equations of motion to fully understand the movement of these particles.