Math probblem of the week

from Wired:

Could Tauriel shoot an orc arrow out of the air?

With this estimate, Tauriel is just 5 meters from the orc and about 9 meters from Legolas. In order to hit the arrow fired from the orc, I would estimate that Tauriel would have to fire AFTER the orc fired. Suppose she has lightning fast reaction time and can aim and fire in just 0.05 seconds. This would mean that her arrow has to travel 9 meters in just 0.05 seconds giving it a speed of 180 m/s. Yes, that’s fast. Right now, real humans are trying to break the 400 fps arrow speed (121 m/s). Ok, but she’s an elf. I guess she’s better than modern humans.

more about arrows in flight HERE.

and Outdoor life discusses arrow speeds of compound bows, which commonly shoot 300 fps.

Is 400 Possible?
Yet the question remains: Can a compound bow shooting at the current IBO standards push an arrow to 400 fps? Mathematically, we’re told, the answer is yes. We’ll leave out most of the complicated math tossed at us by egghead engineers, but the bottom line is that while IBO standards place a limit on the maximum amount of energy a fully drawn compound bow can store and potentially release into an arrow, it’s theoretically possible for a 70-pound bow set at a 30-inch draw length to propel a 350-grain arrow at 400 fps....
Unless you’re one of those guys who names his biceps, you must first acknowledge that the compound bow isn’t powered by an engine, but instead is a hand-drawn machine—and at some point, the output from any hand-drawn device will max out.

Tauriel does not have a compound bow, but does have a recurved bow, which is usually made of several componants glued together and more powerful than a plain wooden bow.

So she must have some pretty good biceps to get that type of speed (duh)