While Phoenix is frequently claimed to have a range of "over 90 nautical miles" or even longer, those range figures refer to the range at time of launch against a target approaching head-on; the target is being kind enough in this case to close the range about 20nm over the flight time of the missile. A more realistic range figure for the AIM-54 would be about 70nm, and at the outer end of that range, the missile is coasting, and would have a rough time intercepting a nimble target like a fighter (though it might do well against a bomber or ASM, which is what it's designed to shoot at anyway).

The moral of the story is that you should turn away and run like hell when a Tomcat paints you with its radar.