Time of closest approach between two particles

[Davidllerenav]

Yes. But you are only looking for the minimum distance between them. In the figure on the right in post #23, can you draw the line of motion of 2 in this frame of reference? Can you identify the point on the line of motion that corresponds to the minimum distance between them?

It would be a line that goes through the velocity vector. I think that the point that would corresponds to the minimum distance would be when the point 1 and the line of motion of 2 make a prepedicular line, right?

 

[TSny]

It would be a line that goes through the velocity vector. I think that the pint that would correspond to the minimum distnace would be when the point 1 and line of motion of 2 make a prepedicular line, right?

Yes, if I'm interpreting what you said correctly.

 

[Davidllerenav]

Yes, if I'm interpreting what you said correctly.

Ok. so I have to make a triangle, right? But what would be the sides? One would be unknown since it is the minimum distance. What about the other two? I think that one would be the distance at time $t=0$ and the other the line of motion of 2.

 

[TSny]

Ok. so I have to make a triangle, right? But what would be the sides? One would be unknown since it is the minimum distance. What about the other two? I think that one would be the distance at time $t=0$ and the other the line of motion of 2.

I don't believe that the line segment representing the initial distance between the objects will be of use. If you've drawn the trajectory of 2 and the line segment representing d_min, you might see two right triangles that you can work with.

 

[BvU]

when the point 1 and the line of motion of 2 make a prepedicular line

show us in the drawing ...

 

[Davidllerenav]

Ok. so I have to make a triangle, right? To find the minimum distance.

I don't believe that the line segment representing the initial distance between the objects will be of use. If you've drawn the trajectory of 2 and the line segment representing d_min, you might see two right triangles that you can work with.

show us in the drawing ...

Like this?

 

[TSny]

Like this?

Yes. You can work with the two right triangles in the diagram to find d_min.

There are other geometrical constructions that can be used to get the answer, including constructions that do make use of the line between the two initial positions of the objects. So, you should explore various approaches.

 

[Davidllerenav]

Yes. You can work with the two right triangles in the diagram to find d_min.

There are other geometrical constructions that can be used to get the answer, including constructions that do make use of the line between the two initial positions of the objects. So, you should explore various approaches.

Thanks, I will look for other ways.

 

[kuruman]

Thanks, I will look for other ways.

You might also wish to consider that in the reference frame where object 1 is at rest at the origin, the angular momentum of 2 about the origin is conserved. This means that the initial angular momentum is the same as the angular momentum at the point of closest approach.

 

[Davidllerenav]

You might also wish to consider that in the reference frame where object 1 is at rest at the origin, the angular momentum of 2 about the origin is conserved. This means that the initial angular momentum is the same as the angular momentum at the point of closest approach.

I haven't seen momentum in my class yet.

 

[kuruman]

You don't really need it but it's a compact way to express what diagram to draw. It involves making use of the line between the two initial positions of the objects as @TSny suggested in #37.

 

[PhysicsKT]

What is galilean transformation? I was able to do this problem easily using maxisimation of a function using differentiation. It's from I.E. Irodov.

 

[BvU]

What is galilean transformation? I was able to do this problem easily using maxisimation of a function using differentiation. It's from I.E. Irodov.

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