Posted by tpc at February 22nd, 2007
What’s the difference between jumping down from the 2nd floor versus the 20th floor?
Ans:
Splat! Aaaaaaahhhhh! (2nd floor)
Aaaaaaaahhhhh! Splat! (20th floor)
What if you jump from the 10th floor? It all depends on how long you remain in the air. A little calculus (plus some physics) does the trick.
Let v be your velocity and u be the initial velocity which is assumed to be zero. That is you gently let yourself off the edge instead of making running jump. Of course a will be acceleration 10 m/s^2. Let’s not be fussy about precision.
Let t_s, i.e. time_splat, be the time you hit the ground and d the distance covered. We have

Now let’s assume average height per floor is about 3 metres, so d = 30 gives
.
About 2.5 seconds, I guess enough for Aahh!Splat!
There you have it, who says calculus is useless?