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Unfortunately there are several mistakes in the text of problem #4. The formula is indeed supposed to give the collision time. In fact there is also parts of the formula missing. This shows up when you do the dimension analysis. When using the formula as it stands, the results obtained are not realistic. You will have to regard this as an exercise in applying a methodology for solving these type of problems, don't pay attention to the numerical result obtained.

When I checked the dimensions I got kg/s.

I used e0 = [F/m] = [s^2*c^2/(m^2*kg), but still, it isn´t in seconds...