(there is supposed to be a movie about boredom here. i can't find a working file. if anyone has it, (boredom.mov), i will love you long time for a copy. thanky.)
Responses to last week's Wrath of the Math column:
First of all, I will admit the question was bunk. I didn't just drop off the wall, I jumped up into the air. So, unless you knew the exact force I jumped with and the angle of my takeoff, you couldn't do much but estimate from the point where my Y-axis velocity was 0 (the apex). By my count, it was 18 frames, although I was technically 'in the air' for 20. I don't have any idea where people got 21, but what can you do.
Even if you had the right frame count, you would know the height from which I fell, not the height of the wall. Basically, you had to do some estimation and guess work, and everyone knows that doesn't count as "math". That is "magic", and magic is a dangerous path indeed. Let it go.
My mathematical guess before I measured was:
d=1/2(32ft/s^2)*(18/15)^2= 23ft minus a few feet for the jump.
Basically, between 20-23 feet.
The official measurement (with a tape measure) was 22ft. Yay! No one answered the problem correctly, but I was happy anyone even paid attention. Here are the details of a few entries:From: Matt LyonThanks for the responses. You are all beautiful, intelligent people, despite your wrong answers. I'm feeling particularly saucy today, so turds for everyone who answered! See you guys at the Long Beach Grand Prix this weekend, I'm driving the pace car.
1G (the rate shit falls at) = 32ft/sec^2
You took 21 frames to fall in the pool. At 15 frames/sec, that's 1.4 seconds.
d=32(ft/s^2)*1.4(s)^2 / 2, which
equals something like... 31.36 feet. Or 9.6 meters if you're doing it the metric way.
Pretty good fall, we don't have anything that tall around here that would let us land on anything other than asphalt, gravel, or hard-packed dirt. I ain't about to do that, and besides, you don't need the media breathing on you saying 'internet cult caused stupid kid to jump to death', do you?
Don't worry about us. If you go for that jump, just make sure you send in the footage. -slap
From: Paul McKay
Your calculation as to the lifting force of a weather balloon is essentially correct but you do need to acknowledge the assumptions which you made which will tend to lower your estimate in real life.
V = (4/3)*pi*r^3 = 36*pi ft^3 for a six foot balloon
P = rho * R * T
rho1*R1 = rho2*R2
rho1 = rho2*R2/R1
R2/R1 = (Runiv/m2)/(Runiv/m1) = m1/m2
rho1 = rho2*m1/m2
Given that m1 = 4.0026 and m2 = 28.9644 and rho(air) = 0.002378 slugs/ft^3 at sea level on a standard day then
rho1 = 0.002378slugs/ft^3 * (4.0026/28.9644) = 3.286166E-4 slugs/ft^3
thus the bouyant force on the balloon is
F = V * (rho2 - rho1)
= 36*pi ft^3 * (0.002378 slugs/ft^3 - 3.28616E-4 slugs/ft^3)
= 0.233167 slugs
converting to the more familiar unit of pound-mass (lb-m) the balloon will lift a maximum of 7.45 lb-m.
Recall that this is a maximum number. The greater the inflation pressure of the balloon the lower the lifting force will be. Also recall that the balloon will not be round but will occupy somewhat less volume due to distortion effects. As the pressure inside the balloon increases the balloon will tend more towards a round shape but the bouyancy loss due to the increase in pressure will tend to counteract the gains due to the increase in volume. The ideal inflation would have to be found by trial and error. You should also consider that the balloons will have to lift not only your weight but also the weight of the balloons themselves plus your harness plus the cords securing the balloons to the harness plus (I assume) your video camera.
I do not have a quicktime plugin for my browser (it is hard to get plugins for SGI machines) but the solution to your falling problem will be: distance fallen (in feet) = (1/2) * 32.3 ft/s^2 * (frames falling / 15) ^2
Paul here did a lot of work, but came up with basically the same answer for the balloon problem. Go figure. But I hear where you are coming from Paul, life is not always perfect. Unfortunately, Paul had the right jump equation but couldn't see the movie to determine the time airborne! What a world! -slap
From: mandeep gill
i count 21 frames, which at 1/30 of a frame a second is .7 seconds, which using d=1/2 a t^2 since you're jumping almost horizontally, would only give about 7.2 feet, which is definitely too small, so either the film to mpeg changes the frame speed or something. if it does, to say 1/15 sec per frame, the distance goes up to 29 ft, which is now too high judging from the visuals. it's somewhere in between though. hope someone else has sent in the right anwer.
It was 1/15 sec per frame, but you also counted 21 frames. Hm. Good visual judgment though. -slap
From: Greg Magnus
OK, all I could figure out was that it was about 20 frames for you to hit the water. If you camera is 15 frames per second that means you were in the air for approximately 1.3 seconds.
The only formula I know is velocity is something like 9.8 meters per second (squared) so when I did the math that wall is almost 13 meters tall -- around.... just found the conversion thingee... 41 feet??? no way.
see. all that crack is taking its toll. knew i wasn't sciece major stuff.
but i do need to know how tall the wall was.
There is nothing wrong with a little recreational drug use, just don't let it get in the way of your studies. -slap
i checked out yer new LOP, titled after Jeru da Damaja's new album.
i was pretty into it cuase when i was little, i tied a helium balloon to a spoon, made it float. and then figured, hey, i can make myself float. i think i weighed 38 pounds at the time.
which made me think of a way you can cut yer costs:
ok if 1 helium balloon can make 1 spoon float.
lets say that 1spoon = 1 ounce = 1 balloon.
then 16 balloons will make 1 pound float.
you need to make 93 pounds float (half yer weight) = 1,488 balloons.
then let's say you can get a pack of 16 balloons for $1.00.
1,488 balloons = $93.00
then get rid of the harness, cause fuck, just tie all the balloons to yer belt buckle, and you just saved yerself $152.00. ha! i think.
you'll have to wear a belt with the red jumpsuit...not so cool looking, but maybe worth it.
Genius! Bold, fashion conscious thinking indeed!
-- slap maxwell