[Varyon]

I should note that your swordsman is sprinting at 40 miles an hour. Why are you throwing an amateur archer up against a superhuman speedster?

That said, using a bow requires high skill, some patience, and range. The big advantages are that an arrow cannot be Parried (without cinematic abilities), which is typically the foe's best defense, and that you can actually reach out and touch your foe without getting close enough for them to strike back. Let's start our opponents only 50 yards apart (a more likely engagement range) and make our swordsman be sprinting at only Move 6 (appropriate for a character with Move 5 and No Encumbrance). The first round, our archer is at -8 to hit (you typically don't count human-scale movement for Speed penalties, and personally I think only lateral movement should really matter there anyway), so he'd need Bow 17 and go All Out for a 50% shot (Bow 21 for the general "safe" 91%). Instead of shooting, he Aims, for +3 to hit. Next round, he's still at -8 for Range, but now Skill 14 would be enough for a 50% shot (Skill 18 for 91%). Let's assume he continues Aiming - next round he's at -8+4 (13/17), then -8+5 (12/16). He won't get further bonuses for Aiming, but he can wait for his target to get a little closer, getting +1 for Range on each of round 5 (26 yards out), round 7 (14 yards out), and round 8 (8 yards out), then completely negates the penalty on round 9 (2 yards out). Probably his best bet is to take a shot (with an All Out Attack) on round 4 (at net -2 to skill), reload on rounds 5 and 6, Aim on round 7, then make an All Out Attack on round 8 (at net -1 to skill), and finally draw a melee weapon on round 9. If he doesn't have very good melee skill, or if his foe looks more likely to Slam than attack on round 10 (in which case Parry probably isn't an option), he may be better served holding his second attack until his foe is 2 yards away and using a normal Attack, which will be at a net +4 to skill.

Of course, a single foe charging a single archer isn't the usual place you'll see a bow in use. A good archer will position himself where he's difficult for the melee foes to reach (high ground - which also functionally reduces range to targets - or behind a wall of rubble or defenders), allowing him to rain death with relative impunity. Archers are also useful when the enemy has a ranged unit in a similar situation - it's a lot harder for a swordsman to take out the archers standing on top of the city walls than it is for the archer. Bows are also useful for sneak attacks, as you don't need to get nearly as close before making your attack (and you've got better exit options if things go poorly). In cinematic settings, Heroic Archer can also be of use, as it allows you to, amongst other things, skip Aiming for the bonus, rapid fire your bow (with Heroic Archer and good skill in Fast Draw and Bow, you can attack every round - twice a round if you string two arrows at once for a Dual Weapon Attack).