Determine if a moving object will pass within range of point

Need an algorithm or series of algorithms to determine if a moving
object will pass within set range of another point.

For example, person at 95 W, 41 N walking Northeast at 5mph.

a) will that person pass within [3 miles] of 94.5 W and 41.5 N?
b) if so, when? or estimated time of arrival?

I am familiar with formulas used at Aviation Formulary
(http://williams.best.vwh.net/avform.htm)

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