Why does a repulsive potential proportional to 1/r² give a straight-line orbit?

[Cosmossos]

Hello,
In question 3(b) in the following file
http://phstudy.technion.ac.il/~wn114101/hw/wn2010_hw09.pdf

Why the orbit will be a straight line?
I think that when the particles are coming to r=0 the potential will be infinity, isn't that so?
So the energy will be infinity and e will be infinity... please help me...
thank you

AND ONE MORE THING: if the potential is a/r^2 (>0) then then the two objects will attract each other, right? But in the Gravitational law (-Gm1m2/r^2) the potential is <0 and the objects will attract to each other

 

[Redbelly98]

Hello,
In question 3(b) in the following file
http://phstudy.technion.ac.il/~wn114101/hw/wn2010_hw09.pdf

Why the orbit will be a straight line?

The problem statement explicitly states the particles move "on the x direction" and "on the y direction". Presumably they mean on the x and y axes; it is not worded quite properly but I can't imagine it meaning anything else.

So, each particle moves in straight line simply because the problem statement says that they do. What would actually cause this to happen is not important.

I think that when the particles are coming to r=0 the potential will be infinity, isn't that so?

No, it would be negative infinity in this example.