The　geodesics　of　tunneling　particles　were　derived　unnaturally　and　awkwardly　in　previous　works.　For　one　thing,　the　previous　derivation　was　inconsistent　with　the　variational　principle　of　action.　Moreover,　the　definition　of　geodesic　equations　for　massive　particles　was　quite　different　from　that　of　massless　case.　Even　worse,　the　relativistic　and　nonrelativistic　foundations　were　mixed　with　each　other　during　the　past　derivation　of　geodesics.　As　a　highlight,　remedying　the　urgent　shortcomings,　we　improve　treatment　to　derive　the　geodesic　equations　of　massive　and　massless　particles　in　a　unified　and　self-consistent　way.　Besides,　we　extend　to　investigate　the　Hawking　radiation　via　tunneling　from　Reissner-Nordstrom　black　holes　in　the　context　of　AdS　spacetime.　Of　special　interest,　the　trick　of　utilizing　the　first　law　of　black　hole　thermodynamics　manifestly　simplifies　the　calculation　of　tunneling　integration.