Physics quiz question: Brachiosaurus vomit

Physics 205A Quiz 4, fall semester 2015
Cuesta College, San Luis Obispo, CA

A hypothesis about dinosaur behavior[*] proposes that a Brachiosaurus could regurgitate 50 kg of vomit that would reach the ground with 6,900 J of translational kinetic energy. Ignore friction/drag, assume a zero initial speed for the vomit, and that it drops straight down. The height that the vomit fell downwards was:
(A) 5.3 m.
(B) 14 m.
(C) 22 m.
(D) 28 m.

[*] Anthony J. Martin, Dinosaurs Without Bones: Dinosaur Lives Revealed by Their Trace Fossils, Pegasus Books (2014).

Correct answer (highlight to unhide): (B)

The energy transfer-balance equation is given by:

W_nc = ∆KE_tr + ∆PE_grav + ∆PE_elas,

where W_nc = 0 (no external gains/losses of mechanical energy due to friction/drag), and ∆PE_elas = 0 (no springs involved), such that the remaining terms in the equation are:

0 = ∆KE_tr + ∆PE_grav.

As the vomit fell downwards, its speed increased such that its translational kinetic energy increased, such that its initial-to-final change must be positive: ∆KE_tr = +6,900 J. Then assuming that y_f = 0, we can solve for the initial height y₀ that the vomit started falling from:

0 = +6,900 J + m·g·(0 – y₀),

0 = +6,900 J – m·g·y₀,

y₀ = (+6,900 J)/(m·g),

y₀ = (+6,900 J)/((50 kg)·(9.80 kg·m/s²)) = +14.081632653 m,

or to two significant figures, the vomit fell downwards by 14 m.

(Response (A) is √(2·∆KE_tr/(m·g)); response (C) is √(m·g); response (D) is (2·∆KE_tr/(m·g)).)

Sections 70854, 70855, 73320
Exam code: quiz04w04K
(A) : 2 students
(B) : 58 students
(C) : 10 students
(D) : 1 student

Success level: 81%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.44

"Fig-23"
Anthony J. Martin
esciencecommons.blogspot.com/2014/02/bringing-to-life-dinosaurs-without-bones.html