Let's set that straight: bows are lousy weapons. Welsh longbows are lousy and encumbering.
Throughout the middle ages in Europe there were thousands of battles. Bows were useful in only two of them, both won by the british, and this has made the longbow a sort of mythical status as a medieval uber-weapon in the english-speacken world, just like the absurd glorification of the katana as a superior sword, or the fascination about nazi super-soldiers and super-weapons.
Bows are tools for hunting. They are good to hunt small game from short to medium distances. That's what they are good for. In battle they are next to useless, unless a certain combination of tactics and opportunity concurs.
There's a tendency in fantasy novels and visual media (movies, videogames) to depict bows as the medieval rifle - or even submachine-gun - which is another misconception. Bows were used in battle, when they were used at all, as a primitive form of field artillery. French knights could drank their wine unconcerned by a heavy rain of arrows, but medieval infantry was nothing but peasants armed with forks. Less than one of every ten of them had a shield, less than one of fifty had a sword and absolutely no-one carried any kind of armor. As a result, when in Agincourt or Crézy the welsh bowmen started shooting arrows, they were aiming to the mass of infantry downhill, not to the knights.
Because that's a problem with bows, no matter how powerful or far-reaching: the best bowmen could hit a static human-sized target at a hundred paces 50% of times. What they did was aiming at whole armies, with hundreds at a time. It was carpet-bombing, not sniping.
So the french commanders had three options: retreating from the field, allow their infantry to be massacred until they routed or charge to eliminate the bowmen threat. So they decided to charge uphill against a heavily fortified position. It was pikes, tramps and trenches who defeated the french cavalry. Clever use of the bowmen may have decided those battles, but no knight was ever killed by an arrow.
Bows can be deadly weapons when used like the tribes of the steppe used them. Their bows were far superior to welsh longbows: they required less force to draw, offered comparable strength and reach, where easier to aim and, specially, could be used on horse. By loosing arrows while on the run upon a horse, mongols, huns, scitians and many other peoples of the steppes could run close to their target - otherwise, no matter how powerful the bow, you're gonna miss -, aim carefully avoiding armor and shields, injure the enemy (rarely killing) and run away unscathed.
Even then, bows were used in a war of attrition, forcing the enemy to charge and chase the mounted archers to ambush them and finish them with swords.
So, you want a superweapon for your insanely strong race of supermen? That's easy: a warhammer. If you want a ranged one, a javelin. Optionally with an atlatl for greater reach.