**SPOILER ALERT.** In the movie *The Hobbit: Desolation of Smaug*, Legolas fights some orcs. Yes, Legolas isn't supposed to be in this movie, but he is. At one point, Legolas takes a breather from fighting and some orc thinks this would be a perfect time to take him out with an arrow. The orc's arrow flies towards Legolas, but BOOM. The arrow is shot out of it's trajectory as it is hit from another arrow fired from the wood elf Tauriel.

That's your plot. Now for the physics.

## How Fast Is Tauriel's Arrow?

Looking at the video, there are only a few details I can get. First, it takes about 0.1 seconds for the arrow to go from the orc almost all the way to Legolas (but not all the way). If I know how fast an arrow is fired from a bow, I can use this to get the distance from the orc to Legolas. It seems a decent arrow speed (shot from a modern bow) would be about 100 m/s. Of course the question is - are orc bows as good as a modern bow? Let's say no. Let me put the arrow speed at 60 m/s. That would put the orc-Legolas distance at just 6 meters.

What about Tauriel? I'm just going to estimate the position of the wood elf. Here's a diagram showing the locations. Note: this is just an estimate.

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.

## How difficult would it be to hit that orc arrow?

I will assume the orc arrow is traveling in a horizontal motion. Tauriel has to aim two ways. First, she has to aim vertically in order to hit the arrow. Let me assume the orc arrow has a diameter of 1 cm (and so does the elf arrow). In order to obtain an arrow-arrow hit, the elf arrow has to be in a certain position.

From this, the elf arrow has to be in a 1 cm vertical range to get a clean hit. If the arrow is 9 meters away, this is an angular size of just 0.06 degrees. Is that a small target? Let's say you wanted to hit a 10 cm apple. In order to have the same angular size of the target, you would have to be 90 meters away. So, that seems like a tough (but maybe not impossible) target.