Brian's Blog

I’m not sure what you will find here; general musings and maybe some technical stuff spattered here and there.

Wednesday, May 03, 2006

A Sucker is Born Every Minute

A while ago, probably close to nine or ten months ago, I was sitting in the office of a former co-worker. We would bs a lot, almost 30% of the day was spent bs'ing. Anyway, during one of those bs sessions, I threw out the comment that I could land in the pond if I jumped off the roof of the building. Immediately that comment was shot down as being completely and utterly ridiculous. "Your out of your mind", they said.

Right outside my coworkers office was somewhat of a spectacular view. He had trees, a pond, geese, egrets, some sort of mutant fish, squirrels, rabbits and ducks. It's one of those views you don't take for granted, knowing you will never score an office similar at another company. The pond is about 15 feet from the side of the building, and the building is three stories tall. I said by running at full steam and leaping off the side of the building, your body would carry far enough to hit the pond. It looked very possible to me, and I was surprised by the disbelief. I made myself a note to try and mathematically solve this problem one day and post the answer. We'll I've got some free time, and guess what... I've also got the answer.

There are a couple critical pieces of data you need to solve a problem like this. Knowing these key pieces should be enough to solve our problem.

1. How tall is the building?
2. How far away is the pond?
3. How fast will the person be running off the top of the building?

I know the building is three stories tall. I'm not about to climb to the roof and drop a tape measure to get an exact measurement, so I'll guess. Being that I work in the building, I'm very familiar with it. By guessing, I'll say the ceilings are about 10' tall. Taking into account the space between the ceiling and the floor above, I'll say each floor is about 12'. Thus, 12 x 3 = 36. For my equations I will assume the building is 36' tall.

Using the un-biased guesses of others, the pond is about 12-15 feet from the side of the building. I'll avoid any doubt and say its 15 feet.

8mph is probably somewhere in the neighborhood of my maximum sprint. It's probably not the fastest I can run, but given the limited space on the roof, probably the most I can squeeze out before going airborne. So we'll set the speed at 8mph.

Ok, we have our numbers, now we need the math. I am by no means fluent in math or physics, and right now my education on the subjects is deeply rooted in google. As such, I will not be calculating for drag, so lets pretend I will be jumping in a vacuum.

The first thing we need to do is figure how long it will take me to hit the ground. This value is required to calculate how far my body will travel. The equation below does just that. Note the table denoting what each variable represents.

y = v * t + 0.5 * a * t2

y = Vertical displacement. Basically, how far is the object falling. This will be the inverse of the height of the building (-36ft or -10.97m).
v = initial vertical velocity. Being that I am jumping off the roof, my initial vertical velocity will be 0m/s.
t = Time, or the duration of my flight. This is what we will solve for.
a = Vertical acceleration. On earth, not taking into account drag, everything that falls accelerates at a rate of 9.8m/s/s. Which means for every second of decent in a fall, you will accelerate 9.8 meters per second.

By plugging in our values we get the following.

-10.97m = 0 * t + 0.5 * 9.8m/s/s * t^2
-10.97m = 0.5 * 9.8m/s/s * t^2
-10.97m = 4.9m/s/s * t^2
2.24s^2 = t^2
t = 1.5s

This means I will free fall for 1.5 seconds when jumping off the roof of the building. Thats just enough time for me to crap my pants.

Now that we know the duration of my flight, we can calculate how far I will travel. To do that I'll use the equation below.

x = v * t + 0.5 * ax * t2

x = The distance traveled. This is the value we will solve for.
v = Initial horizontal velocity. Since I will be running 8mph when leaving the roof, this value will be 3.58m/s.
t = Time. We just solved for that. This value equals 1.5s.
a = Horizontal acceleration. I will be running at a constant speed of 8mph, so I will have 0 horizontal acceleration. This value will be 0m/s/s.

Lets plug in the values and solve for x.

x = 3.58m/s * 1.5 + 0.5 * 0m/s/s * 1.5^2
x = 3.58m/s * 1.5
x = 5.37m

According to the math my horizontal displacement will be 5.37 meters, or 17.62 feet. Since we've estimated the pond being 15 feet away, this will put me well into the water upon impact.

I know drag was not taken into account, and if it was it probably would have a considerable effect on the numbers. However, I could also run faster than 8mph, and I could also jump at the end which would add an upward angle to my horizontal velocity carrying me even farther. The bottom line is this: I believe a $500 bet was made stating that I could not make it to the water. I've just proved I can... Pay up!


At 4:38 PM, Blogger J. said...

Good grief you must be board at work. Then again so am I considering I update mine almost every day.

At 9:25 PM, Blogger Mark Deffenbaugh said...

Well I, the former co-worker who occupied the really nice office, think I'll be retaining my $500 because I'd like to see Brian jump through the branches of the trees placed between the building and the pond.

Though, if Brian did make it, the $500 would be worth it to see him land, at that velocity, into 1 or 2 feet of water.

Also, based on the length and thouroughness of this article, I'll bet that Brian has taken my 30% bs time and appended it onto his.

At 10:40 PM, Blogger Brian said...

Well first off, I didn't type it at work. I typed it the other night, and just posted it while at work.

But yes, I am using your 30%.

At 7:22 PM, Anonymous Anonymous said...

Zager would be proud! ;)


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