Dropping coins from the Eiffel Tower

[DB]

Is it true that a coin dropped from the top of the Eiffel Tower or other similar tall structure would gather enough pace on its descent that it would be able to kill someone if it landed on them?

[incitatus]

No. Take a limiting example: a 5p coin dropped from the top of the radio antenna in a perfect vacuum. The coin (mass 3.3g) would attain only about 80 m/s and have a kinetic energy on the order of 20J. Not a lot. Certainly not fatal. But consider that it will not be in a vacuum. As the air drags on the coin it will decelerate and so never gain this energy. You might not want to look up and get one in the eye, but it isnt going to damage you if it falls on your head.

[WaldoMcFroog]

To follow up on Incitatus's answer: In too much detail: http://www.math.niu.edu/~rusin/known-math/99/fallp
enny In not much detail: http://www.straightdope.com/classics/a1_225.html

[xequtive]

I'd guess so, but i wouldn't suggest trying it... due to the acceleration of the coin the momentum will increase enough so that if it hit someone on the head they'd die. My mate once dropped a bouncy ball off the Eiffel Tower once (truly) and i left before i could found out what happened.

[xequtive]

correction- incitatus was probably right, it wouldn't be fatal but it would bloody well hurt.

[incitatus]

It wouldnt even hurt that much Both stop accelerating quite quickly after launch due to friction. 20J (which is the max you could get out of a 5p coin is (if I have my sums right) like a 10 kg weight dropped from 2cm. Bit of an ouch but hardly hospital time unless you have a very weak neck. And remember thats a maximum. You would be unlikely to get even a tenth of that, due to atmospheric friction.