Why Raindrops Don’t Kill Us…Part 2

In the original post about Why Raindrops Don’t Kill Us, I showed why raindrops falling from the sky do not kill us. Some clever reader wondered what would happen with hail — would that inflict more pain than just a drop of rain?

I’ve been thinking about it and have come to the conclusion that hail (which is simply frozen rain, or more dense water) will not cause more pain than just the drop of rain.

This is because terminal velocity is independent of mass. You might argue, saying that F = ma; the force is dependent on mass and acceleration. Try thinking about the force being connected with air resistance, rather than velocity. When a raindrop is falling, it is exerting force on the air around it. According to Newton’s 3rd law, the air will exert an equal and opposite force on the droplet. Therefore, force is negligible for this argument.

What we’re really concerned with is the equation v = v(0) + at, where v is the terminal velocity, v(o) is the initial velocity (in this case, it actually equals zero), a is acceleration (in free fall, a = 9.81m/s^2), and t is time. Rewriting the equation yields:

v = at

Ta da! The terminal velocity is only found by two variables: acceleration (a constant in free fall) and time. So, in theory, hail will not fall any faster than rain. It might hurt more, but that would be a result of the physical properties of the hail (frozen, dense water) and not  because of the speed it has falling from the sky.

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