20140916

Physics quiz question: UCSD Tioga Hall pumpkin drop

Physics 205A Quiz 2, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 2.47

In 2007 a pumpkin dropped from the top of Tioga Hall as part of a long-running Halloween tradition at the University of California, San Diego.[*] The pumpkin fell for approximately 2.3 s before hitting the ground 41.1 m below.[**][***] Neglect air resistance. Choose up to be the +y direction.

"UCSD JMC Pumpkin Drop 2007"
0racleman
youtu.be/2hMCbYwlm3c

The initial (downwards) velocity of the pumpkin was:
(A) –29 m/s.
(B) –28.4 m/s.
(C) –18 m/s.
(D) –6.6 m/s.

[*] Pat Jacoby, "Media Advisory: Annual UCSD Monster Pumpkin Drop," October 29, 2007, ucsdnews.ucsd.edu/archive/newsrel/events/10-07MonsterPumpkinDropPJ-L.asp.
[**] 30 frames at 13 fps, youtu.be/2hMCbYwlm3c.
[***] "Height (estimated): 134.84 ft," emporis.com/building/tiogahall-sandiego-ca-usa.

Correct answer (highlight to unhide): (D)

The following quantities are given (or assumed to be known):

(t0 = 0 s),
(y0 = 0 m),
t = 2.3 s,
y = −41.1 m,
ay = −9.80 m/s2.

So in the equations for constant acceleration motion in the vertical direction, the following quantities are unknown, or are to be explicitly solved for:

vy = v0y + ay·t,

y = (1/2)·(vy + v0yt,

y = v0y·t + (1/2)·ay·(t)2,

vy2 = v0y2 + 2·ay·y.

With the unknown quantity viy to be solved for appearing in the third equation, with all other quantities given (or assumed to be known), then:

v0y·t = y − (1/2)·ay·(t)2,

v0y = (y − (1/2)·ay·(t)2)/t,

v0y = (−41.1 m − (1/2)·(−9.80 m/s2)·(2.3 s)2)/(2.3 s),

v0y = (−41.1 m + 25.921 m)/(2.3 s),

v0y = (−15.179 m)/(2.3 s) = −6.5995652174 m/s,

or to two significant figures, −6.6 m/s.

(Response (A) is (y/t + (1/2)·ay·(t)2)/(t); response (B) is sqrt(2·y·ay); response (C) is y/t.)

Sections 70854, 70855, 73320
Exam code: quiz02T1o9
(A) : 18 students
(B) : 7 students
(C) : 18 students
(D) : 27 students

Success level: 39%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.80

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