A point source isotropically emitting 10^8 fast nuetrons

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The discussion revolves around calculating the fluence of neutrons striking a passenger from a point source emitting 10^8 fast neutrons per second, located 3 meters horizontally from a train track. The relevant equation for fluence is defined as fluence = dN/da. Participants suggest modeling the distance to the train as a function of its velocity and time, using the equation r^2 = 9 + v^2*t^2. There is confusion about how to properly integrate this equation over time to find the fluence experienced by the passenger. The conversation emphasizes the need to consider the passenger's position relative to the point source and the train's movement.
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Homework Statement


A point source isotropically emitting 10^8 fast nuetrons per second falls out of its shield onto a railroad platform 3 m horizontally from the track. A train goes by at 60 mph. Ignoring scattering and attenuation, what is the fluence of nuetrons that would strike a passenger at the same height above the track as the source?

2. Relevant equation
Fluence=dN/da

The Attempt at a Solution


I know you need to write the distance to the train as a function of velocity and time. This can be done by having r^2=9+v^2*t^2. If the person in exactly across from the point source at t=0. I know I need to integrate this equation over some dt from -infinity to infinity but I'm confused as to what integral this goes into.
 
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Maybe you can consider the passenger moving radially away from the point source?
 

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