Dropping a penny on your head from the tallest building in the world

Hannah - This week, we bang our heads together by cracking into a question that Ben Bennett wrote in with... Ben - If we dropped a penny from the top of the burg khalifa in Dubai and it hit somebody on the ground what would the consequences be?

Hannah - So, a penny hitting your head after an approximate 830-meter drop, ouch! Or no effect at all? To find out which, we'll climb to the top of an iconic Cambridge spire with the engineering Don, Dr. Hugh Hunt.

Hugh - So, we're going up clock tower here in Trinity College and it's about 12 meters up to the top and I reckon that if we drop our penny then we could estimate how long it takes to get to the bottom.

Hannah - The Trinity Clock Tower is much smaller than the Burg Khalifa. So, how can it tell us the top speed a penny can drop on your head at? After a short drop, objects start to be opposed by air resistance, so they reach what we call terminal velocity, a steady speed that can't be increased no matter how far they fall. Because we know how fast gravity makes things accelerate, we can work out how fast a penny would fall without air resistance and then see if it reaches terminal velocity even from a lowly vantage point in Cambridge. Over to Hugh....

Hugh - It should take about 1.6 seconds to reach the bottom. If it takes longer than that then we're reckoning that we must've reached terminal velocity.

Hannah - And if it reaches terminal velocity then it will be dropping at the same speed in Cambridge as in Dubai. Speed is important as the faster the penny travels, the harder it hits and the more damage it will do to a head.

Hugh - We better work on the assumption that a penny landing on somebody's head will kill somebody, so we better make sure there's nobody standing underneath. Alright, I've got my penny and I'm going to see if I can work out how fast it takes to go over the edge, 3, 2, 1, go... So, that was about 2 seconds which means that the penny is very definitely reaching terminal velocity, even after a distance of 12 meters. And so, dropping it from a higher tower, my guess is, that it won't be going really much faster than the speed that we saw just then. We're really talking maybe 5 to 10 meters per second which is no more than 15 or 20 miles an hour. It's not that dangerous. You can easily throw the penny that hard and if you were across with somebody and you threw a bundle of coins at them, it might hurt but they're not going to die.

Hannah:: Thanks, Hugh. So, it seems that if we dropped a penny from the top of the tallest building in the world and due to air resistance, the penny would only reach about 15 to 20 miles per hour and Hugh doesn't think that an object with this speed and mass would cause significant damage to your head. That is unless you spin the penny like a spinning wheel then it would slice through the air with far less air resistance, move much faster, and could hit you edge on so it would be much more dangerous.