# What is the terminal velocity of a quarter?

## Main Question or Discussion Point

2 questions:
What is the terminal velocity of a quarter? and How long does it take a quarter to accelerate to its terminal velocity?

Related Other Physics Topics News on Phys.org
Terminal velocity is dependant to the cross-sectional area of the falling quater. Some approximations for the terminal velocity equation are given in a year one university physics text book. Usually in the first few chapters regarding mechanics

russ_watters
Mentor
Mythbusters did a bit on the dropping a penny off the Empire State Building myth. It turns out that because it tumbles, the terminal velocity of a penny is relatively low - on the order of 100mph. I think a quarter would be pretty similar, and they would reach terminal velocity pretty quickly - within 10 sec or so.

Has someone been reading "house of leaves" by any chance?
If so i reckon the calculation is wrong in the book.
Anyway, you can use this formula

Code:
     _____
V= \/ 2 m g
-----
p A C
(thats the square root of 2XmassXgravity / density of fluid(air)XareaXdrag )

Hope this helps :)

PhanthomJay
Homework Helper
Gold Member
2 questions:
What is the terminal velocity of a quarter? and How long does it take a quarter to accelerate to its terminal velocity?
If you do a theoretical calculation for the terminal velocity of a quarter, it'd only be moving at about 30 or 40 mph or so at best if it were falling flat heads or tails up. If that same quarter however was to fall edge side down, it'd be on the move much faster (maybe 100mph or thereabouts absolute tops), since there'd be less area exposed to the 'wind', and hence less air resistance. Because it will spin as it falls, as noted above, it's actual terminal velocity is likely somewhere in between. I once knew some mischievous boys who chucked a penny off the 86th floor of the Empire State Building (I've heard they've since enclosed the balcony), and as far as i know, there were no injuries below or broken windshields or sidewalks. But I think the penny may have bounced off the side of the building on its descent, though, further slowing its fall.
In terms of the time it takes to reach that speed, actually, it never does, but it will approach that speed in probably less than 10 seconds (as also previously noted by Russ.)
Now here's a fun way to determine the approximate terminal velocity of the quarter: Since terminal velocity occurs when the objects weight is equal to the air resistance force, tape a piece of string to a quarter and have a passenger in your car hold it out the window. Then start driving, and the quarter will swing away towards the back. When that angle of swing reaches 45 degrees...bingo! record your constant speed (no acceleration please at time of recording), and you've got the approximate terminal velocity, since at 45 degrees, the wind and weight forces are equal. Drive safely, and do not exceed the posted speed limit. Hmmm, think I'll try that.....

Last edited:
rcgldr
Homework Helper
If the coin was tossed from high enough (1000 feet?), the increase of air resistance due to higher density at lower altitudes may result in the coin reacing a true terminal velocity, and then slowing down before it reached sea level.