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Well, here we are again, in front of that black board. But today's reminder is about the very acceleration you get when falling down to some dodgy impact destiny, and how you can cope with it on a bike. This is the only in-depth physics lecture you'll get on the web, regarding the landing theory of bicycles. And I reckon it's quite clear.

Graphical analysis: a physical explanation of why you can jump from higher on a bike than on your bare feet.

Gravity rules: the speed of impact when launching a drop off.
At what speed will you smash your rear wheel on the rocky bit that you didn't see when dropping off? Here is the theory. Although this is stricly right in vacuum, we'll consider that for the heights we're dealing with, air resistance does not play a major role.

Try the crash Speed calculator
Enter any drop off height value (in meters)

click return to see the results

  Type something useful, else I will crash...
(Crash Speed Calculator not very happy about his job)

Gravity Rules: in theory
When falling freely, a body undergoes the gravity acceleration (a=9.8m/s*2), that increases the body's speed. Hence for a fall of duration (dT) in s, the variation in speed (acceleration) is:

(1): dS=a*dT or a=dS/dT
But the speed (in m/s) is also defined as the distance dH (in our case the height of fall in meters) divided by the time slot (dT) it takes the body to fall from dH.
Hence (2): S=dH/dT

Of course, from expression (1) and (2), we get
(3): a=dS/dT=dH*2/dT*2

By integrating the expression (3) twice on the variable T, for a total height H, we obtain
(4): T*T=2Ha

wich is equivalent to say:
(5): T=square root(2H/a)

where T is the time of fall in seconds, from an height H in metres.
Replacing dT by the expression (5) in the expression (1) gives the speed of impact
(6): S = square root (2aH) = square root (19.6*H)
The speed of impact on landing S, is in metres per second and H, the height of the wall is in metres. On Earth a=9.8m*s-2
To get the resulting speed in kilometres per hour, multiply by 3.6
To get the resulting speed in miles per hour, multiply by 2.237

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