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## Main Question or Discussion Point

1) On a recent exam, one of the questions asked to find the minimum speed at which you would have to fire two protons head-on if you wanted them to get them within [itex]10^-15m[/itex].

To make things a bit easier, I treated one proton as being stationary and then found the energy needed to bring the other from infinity to the specified distance by integrating the coulomb force over that distance. From that I got the velocity which was larger than c but double the minimum speed of each proton. Is this approach valid? I wasn't too sure because of accelerating frames of references involved...

2) It also got me thinking about what would happen if two objects were moving towards each other at, say, 2/3 the speed of light. Wouldn't each appear to the other as moving faster than light?

To make things a bit easier, I treated one proton as being stationary and then found the energy needed to bring the other from infinity to the specified distance by integrating the coulomb force over that distance. From that I got the velocity which was larger than c but double the minimum speed of each proton. Is this approach valid? I wasn't too sure because of accelerating frames of references involved...

2) It also got me thinking about what would happen if two objects were moving towards each other at, say, 2/3 the speed of light. Wouldn't each appear to the other as moving faster than light?