《那些古怪又讓人憂心的問題》第114期:無重力射箭(1)
WEIGHTLESS ARROW
Q. Assuming a zero-gravity environment with an atmosphere identical to Earth's, how long would it take the friction of air to stop an arrow fired from a bow? Would it eventually come to a standstill and hover in midair?
Q．假設有一個地方的大氣條件和地球上的完全一致，但那裏沒有重力，如果我在那兒射出一支箭，那麼這支箭要多久纔會由於空氣阻力而停下來？到最後這支箭會完全停下來並懸浮在半空中嗎？——Mark Estano
——馬克•埃斯塔諾
A. IT'S HAPPENED TO ALL of us. You're in the belly of a vast space station and you're trying to shoot someone with a bow and arrow.
A．我們每個人都有這樣的經歷。你現在正在一個巨大的空間站表面，準備用弓和箭朝某人射擊。Compared to a normal physics problem, this scenario is backward. Usually, you consider gravity and neglect air resistance, not the other way around.1
和普通的物理問題相比，這次我們的思路要反一反。通常來說你會考慮重力而忽略空氣阻力，但這次我們要忽略重力而考慮空氣阻力。1As you'd expect, air resistance would slow down an arrow, and eventually it would stop . . . after flying very, very far. Fortunately, for most of that flight, it wouldn't be much of a danger to anyone.
就像你預期的那樣，空氣阻力會使箭支減速，最終在飛行了很遠很遠的距離後……箭支會停下來。還好在大部分飛行時間內，這支箭都不會對旁人造成太大的威脅。Let's go over what would happen in more detail.
讓我們仔細看一下整個過程。Say you fire the arrow at 85 meters per second. That's about twice the speed of a major-league fastball, and a little below the 100 m/s speed of arrows from high-end compound bows.
假設你以每秒85米的速度射出一支箭，這個速度差不多是棒球大聯盟飛得最快的快球速度的2倍，和高端複合弓射出的每秒100米的箭相比還差一點。The arrow would slow down quickly. Air resistance is proportional to speed squared, which means that when it's going fast, the arrow would experience a lot of drag.
射出的箭的速度很快就會降低，因爲空氣阻力正比於速度的平方，這意味着箭支在高速飛行時會受到相當大的阻力。After ten seconds of flight, the arrow would have traveled 400 meters, and its speed would have dropped from 85 m/s to 25 m/s; 25 m/s is about how fast a normal person could throw an arrow.
射出10秒後，箭支飛過了400米的距離，速度從起初的每秒85米降到了每秒25米，差不多相當於一個普通的人用手扔出的箭的速度。At that speed, the arrow would be a lot less dangerous.
在這個速度下，飛行的箭支危險性大大下降。We know from hunters that small differences in arrow speed make big differences in the size of the animal it can kill. A 25-gram arrow moving at 100 m/s could be used to hunt elk and black bears. At 70 m/s, it might be too slow to kill a deer. Or, in our case, a space deer.
從獵人那兒我們知道，箭支速度的微小差異會極大影響到被射殺的獵物的體型。一支以每秒100米速度飛行的25克重的箭能夠獵殺馬鹿或者黑熊，而速度每秒70米的箭支可能都無法殺死一隻鹿，或者，在我們的場景裏，太空鹿。
