Speed of a meteor before hitting a space station

[andreea_a]

What is it, symbolically, in terms of the pre-collision velocities of the meteor and space station?

Use conservation of momentum. The total momentum, as a vector quantity, is conserved across the collision event.

But I've done that...in the previous posts. The problem is that I have 2 unknowns. In order to get $v_f$(velocity station+meteor after impact) I must know $v_1$(initial velocity of the meteor)

 

[Simon Bridge]

Would it be easier to be more mechanical about this? i.e.

There are three stages.
I. just before the collision
II. just after the collision
III. on reaching perigee

You should have written an explicit statement for the tangential and radial velocities of each object at each stage.

You should have an expression relating each stage by conservation of energy and conservation of momentum. This gives three sets of equations.

Which quantities are conserves between each of the cases?This should give you something like 8 equations and 8 variables depending on your notation convention. The next step is simplification and cancellation.

i.e. Most of the variables will have a trivial relationship to each other or known values ...
eg. At stage I there is one unknown out of four velocities:
1. tangential velocity of satellite: given;
2. radial velocity of satellite: infer from "circular orbit";
3. tangential velocity of meteor: infer from it's trajectory;
4. radial velocity of satellite: unknown
etc.

When you get used to this sort of calculation, you get used to anticipating some of the results by your choice of notation and which quantities you write an expression for. When you are still struggling, it can be a big help to write down everything, be pedantic. It can help to use a large window and a dry-erase marker as you get to see all the setup relations in one place, and you can rub out mistakes and when you want to make substitutions.

I shall now return you to your regular programming...

 

[D H]

The problem is that I have 2 unknowns. In order to get $v_f$(velocity station+meteor after impact) I must know $v_1$(initial velocity of the meteor)

You are making this problem much, much harder than it is.

In post#21 you wrote

This is what I've got so far:
Applying the conservation of linear momentum for the space station and the meteor:
$$\vec{p_i} =\vec{p_f} => m_1\vec{v1}+m_2\vec{v2}=(m_1+m_2)\vec{v_f}$$

What happens when you divide both sides of this expression by $m_1+m_2$?