If a 5-kg pumpkin is tossed through a snowstorm such that it reaches the peak of its trajectory one meter above the roof of the Green Building, which is 90 meters tall, with what velocity does the pumpkin meet the ground in McDermott Court? How much time, in seconds, does the airborne pumpkin have to come to terms with its identity* before landing? You may neglect wind, viscous drag, and the altered aerodynamics of cold, wet pumpkins for the sake of simplicity.
This past weekend’s wind and snow left over three million homes and businesses throughout the Northeast without power but promptly turned into a miserable deposit of slush when it hit Boston. Sometime after midnight on October 30th the slush mixed with the remains of over 100 shattered pumpkins in McDermott Court below the Cecil and Ida Green Building.
The Green Building, MIT's Building 54, was built on stilts in 1964 to circumvent Cambridge’s height limit. At 21 stories and 90 meters the Green Building became and remains the tallest building in Cambridge. Every October, First West, the smallest hall in the East Campus dorm, drops some large number of pumpkins—two dozen last year, over 100 this year—off the roof in front of lots of hosed, enthusiastic, and, this year, really cold, fellow MIT students.
On the left is my footage of the event. To the right is Isaque '15’s version, which is much higher quality. Full screen and watch both for maximum experience. Happy Halloween, and best of luck to those of you applying EA tomorrow. =)
* Curiously enough, the only thing that went through the mind of the pumpkin as it fell was, “Oh no, not again.” Many people have speculated that if we knew exactly why the pumpkin had thought that we would know a lot more about the nature of the Universe than we do now.
Comments (Closed after 30 days to reduce spam)
Posted by: Jake Stevens on November 1, 2011
Posted by: Daniel Oñate on November 1, 2011
Posted by: D.a.D. on November 1, 2011
Isn't this a bit wasteful? There are people that need the food.
Posted by: Or G. on November 1, 2011
I guess there are people that need the food, but, when you think about it, 100 or even 1000 pumpkins isn't going to do much-- it'd just be a band-aid at best. On the other hand, what the people launching the pumpkins are capable of achieving is much more substantial than giving a village a single pumpkiny meal... .Not to say that charity is bad or anything, but if flying pumpkins make them more capable of actually doing something to help those in need, then I'm all for the waste
Oh, and i <3 the guide n_n
( just noticed the troll name -.- )
Posted by: Jéan-Lé on November 1, 2011
Sure, it's not much, and the people dropping the pumpkins are capable of giving back much more, but dropping the pumpkins does not help them reach that goal in anyway, and helping the needy does not justify wastefulness.
Posted by: Or G. on November 1, 2011
We 'waste' many things in the name of recreation and many more resources without thinking about it... We literally throw away a lot more food each day than the pumpkins you saw in the video above.
As for needless wastefulness, you can't deny that the audience seen we're enjoying themselves... laughter is needed :/ I get that you see people throwing away food, even if it is in an admittedly creative fashion, but at the end of the day, it's activities like this that help them actually help others... Much more than 100 pumpkins... more lasting than temporary aid...
Posted by: Jéan-Lé on November 1, 2011
Posted by: Jéan-Lé on November 1, 2011
<3 the post, and the Hitchiker's reference Lydia! I may well scrawl "don't panic" on my hand for my test on Wednesday.
Posted by: Avanti - 1st Wester on November 1, 2011
You are almost right but since we are not to forget significant figures, and the only ones given to us are the 5 and the 90, we are left with a velocity of 40m/s when the pumpkin hits the ground while taking a nice 9 second trip to think about his demise. Though this is reduced to just under 8 seconds if we assume the pumpkin holds a human reaction time of ~0.7 seconds.
Hope to watch this event next year if I get into MIT.
Posted by: Brandon Rangel on November 1, 2011
I guess we'll just have to agree to disagree.
@ Avanti
Thank you for clarifying that.
I haven't really commented on the rest of the post yet. Loved the THGTTG reference, and your drawing style is entertaining as always!
Posted by: Or G. on November 1, 2011
The object's mass has no effect on the final result, and it's 91 metres.
h = 0.5gt^2
91 = 4.903325t^2
t^2 = 18.5588351
t = 4.30799665
v = gt
v = 10 * 4.30799665
v = 43.0799665m/s
Posted by: Or G. on November 1, 2011
Posted by: Or G. on November 1, 2011
My velocity was the same in my calculations, but I was sticking to significant figures, a concept drilled into my head at my school.
And as for your time, you calculated the time of descent but if you wanted to calculate for the ascent portion, determining the entire trip that the pumpkin had from toss to splat, you would multiply the time you gave by 2. Which was why my answer equated to ~9 seconds.
The lower than 8 seconds was me being funny about a pumpkin thinking like a human.
Posted by: Brandon Rangel on November 1, 2011
Touché, but I'm pretty sure the pumpkin was tossed from a height of 90 metres rather than 0 metres, which would add this much time:
h = 0.5gt^2
1 = 4.903325t^2
t^2 = 0.203943243
t = 0.451600756s
For a total of 4.75959741s.
If reaction time is taken into account, the time the airborne pumpkin would have to come to terms with its identity before landing is 4.54459741s, as the average human reaction time is lower than the time you stated, it's approximately 215 miliseconds.
Posted by: Or G. on November 1, 2011
Well, thank you for correcting my error. My physics teacher and I misread the initial scenario. Still, fun to have the discussion
Posted by: Brandon Rangel on November 1, 2011
It's been a pleasure
Posted by: Or G. on November 1, 2011
One thing, the problem doesn't actually specify where the pumpkin was tossed FROM, it just said the peak of the trajectory was 1 meter over the 90 meter Green building, from which I would assume that it started from the ground.
Oh, and isn't aerodynamics irrelevant if you discount wind resistance? Because aerodynamics is just how air reacts to the object, isn't it?
Posted by: Brandon J. on November 1, 2011
@Jake: Thank you!
@Papa: Thank you! I'm not sure if or how many of the pumpkins were frozen in liquid nitrogen.
@Avanti: Oh gosh, that must have been so much work. You guys rock. Did you freeze the pumpkins in liquid nitrogen before dropping them?
Good luck on your exam!!! Bring a towel.
@Daniel, Brandon, Or G.: The velocity of the pumpkin as it falls to the ground is 42 m/s, the same velocity as a whale or a bowl of petunias would experience. The amount of time the pumpkin has to come to terms with its identity is, to quote Douglas Adams, "very little time": 4.3 s descending + 0.5 s ascending = 4.8 seconds of thought. We can check this by looking at 2:13-ish in Isaque's video. Note that we are assuming that the people throwing pumpkins from the roof of the Green Building are bent over completely to throw the pumpkins from foot level, which sounds almost as uncomfortable as standing on the roof of the Green Building in cold sleet.
@Brandon J.: Pumpkin catapults sound fun. Is that for a class?
The pumpkins were thrown from the roof of the Green Building, not from the ground (though throwing 5-kg pumpkins 91 meters in the air would be a pretty excellent feat). When I specified that we are neglecting wind I was thinking more of any vertical component of force exerted by the wind on the pumpkin. In other words, there are no updrafts or downdrafts.
Posted by: Lydia K. '14 on November 1, 2011
Posted by: Brandon J. on November 1, 2011
(Well, didn't include more info to the reference because it would become a spoiler)
Posted by: Danilo on November 1, 2011
Oh yes, I see my error now, I used g = 9.80665 to calculate the time but then switched to g = 10 to calculate the velocity. If I stick to g = 9.80665 I get the following result:
v = gt
v = 9.80665 * 4.30799665
v = 42.2470153 ≈ 42m/s
Posted by: Or G. on November 3, 2011
42 is The Answer!!!
Posted by: D.a.D. on November 5, 2011
Posted by: Keith on November 8, 2011
@Or G. (and D.a.D.): I'm pretty sure you can't get g to that level of precision without taking Boston's latitude into account, but yes! 42 is the answer. =)
@Keith: That.
Posted by: Lydia K. '14 on November 8, 2011
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