Physics quiz question: comparing BASE jumper energy changes

Physics 205A Quiz 4, fall semester 2016
Cuesta College, San Luis Obispo, CA

"KL tower base jump 2012 | Kuala Lumpur | Malaysia"
enshahdi
flic.kr/p/df5Nwd

A "BASE[*]" jumper (total mass of 88 kg with equipment) reached a final terminal speed of 53 m/s after falling 452 meters downwards (before using his parachute)[**]. Drag is not negligible, assume a zero initial speed, and that he dropped straight down. For this process, the decrease in gravitational potential energy of the jumper was __________ the increase in translational kinetic energy of the jumper.
(A) less than.
(B) equal to.
(C) greater than.
(D) (Not enough information is given.)

[*] Jumping off of a "building, antenna, span, or Earth (i.e., cliff)."
[**] johnnyutah.com/freefallchart1.html.

Correct answer (highlight to unhide): (C)

The energy transfer-balance equation is given by:

W_nc = ∆KE_tr + ∆PE_grav + ∆PE_elas,

where ∆PE_elas = 0, as there is no spring involved in this process. Note that on the left-hand side of this equation, the non-conservative work done by the non-neglible drag force against the BASE jumper is:

W_nc = (F_drag·cosθ)·s,

and must have a negative value, as the tail-to-tail angle between the upwards drag force and the downwards displacement is θ = 180°, and cos(180°) = –1. (Note that the weight force on the BASE jumper is a conservative force, and is already included in the ∆PE_grav term on the right-hand side of the equation, so the work done by this force is not explicitly considered here.)

Since the left-hand side of the energy transfer-balance equation is negative, then:

(–) = ∆KE_tr + ∆PE_grav,

such that decrease in gravitational potential energy (∆PE_grav is negative) must be greater than the increase in translational kinetic energy (∆KE_tr is positive).

Sections 70854, 70855, 73320
Exam code: quiz04th1R
(A) : 13 students
(B) : 16 students
(C) : 22 students
(D) : 0 students

Success level: 43%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.82