Pumpkin Drop by Lydia K. '14, MEng '16
Trick-or-treating is not enough.
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 top is my footage of the event. On the bottom 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.
@ Jéan-Lé
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.
Love the Hitchhiker’s reference!
@ Or G
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…
audience were* -.-
42.2326887612 m/s?!?!
If we neglect the aerodynamics and such, the 5-kg pumpkin has the same time to come to terms with its identity as the whale does. Or petunias. Love the post. Did they freeze the pumpkins in liquid nitrogen? They should have…
For the people talking about wastefulness, the only reason we had > 100 pumpkins was that they were mostly rotten, hence cheap. The brave pumpkin buyers even salvaged a number from a compost heap.
<3 the post, and the Hitchiker’s reference Lydia! I may well scrawl “don’t panic” on my hand for my test on Wednesday.
@Daniel
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.
@ Jéan-Lé
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!
@ Daniel
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
*@Brandon
@Or G,
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.
@Brandon
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.
@Or G
Well, thank you for correcting my error. My physics teacher and I misread the initial scenario. Still, fun to have the discussion
@ Brandon
It’s been a pleasure
Damn, you guys, you took my reply ideas!
Isn’t this a bit wasteful? There are people that need the food.
I would mess with the equation (it’s actually not that hard, we had a chapter over projectile motion pretty recently), but I just spent a day wrestling with a catapult to LAUNCH some pumpkins. We started way too late, and we thought a catapult would be easier than a trebuchet (WRONG), so we barely managed to make it go the required distance of 35 ft >.> (Last year there was a group that managed to go.. 180 yards, and accurate enough to make a field goal from the opposite end zone)
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?
Thank you, everyone, for the kind comments. I’m thrilled that you actually did my physics problem. You guys make my day. =)
@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.
@Lydia Yep, it’s our major physics project for the semester (I believe we build a small bridge next semester). Even the pre-AP classes do it, it’s pretty much an all-day event, with probably almost a hundred kids involved.
@ Or G
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 -.- )
Were you, by any means looking at the pumpkin and stepped on a snail recently? That would explain the pumpkins thoughts.
(Well, didn’t include more info to the reference because it would become a spoiler)
@ Lydia
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
Come on, it just has to be 42… If it’s not, we have to move to the equator, move to another planet, order another planet if we have to, but it has to be 42.
42 is The Answer!!!
What do you mean? An African or European pumpkin?
@Danilo: I would hate for a pumpkin to plot to kill me. It would be the worst Halloween.
@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.