Physics quiz question: Space Shuttle "Launchbat"

Physics 205A Quiz 4, spring semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 6.22

"319336main_STS-119Bat4.jpg"
NASA
nasa.gov/mission_pages/shuttle/shuttlemissions/sts119/launchbat.html

An injured free-tailed bat (mass 0.012 kg[*]) latched onto the external fuel tank of the NASA Space Shuttle Discovery during liftoff[**] from sea level. Assume that g = 9.80 m/s² throughout this trajectory. If the bat held on until the external fuel tank separated from the Space Shuttle at an altitude of 110 km[***], the increase in gravitational potential energy of the bat was:
(A) 0.059 J.
(B) 6.5×10³ J.
(C) 1.3×10⁴ J.
(D) 1.4×10⁹ J.

[*] "12.3 g (0.43 oz)," wki.pe/Mexican_free-tailed_bat.
[**] "NASA—Bat Hung onto Shuttle During Liftoff," nasa.gov/mission_pages/shuttle/shuttlemissions/sts119/launchbat.html
[***] "59 nautical miles," spaceflight.nasa.gov/shuttle/reference/basics/index.html

Correct answer (highlight to unhide): (C)

The increase in gravitational potential energy of the bat is:

∆PE_grav = m·g·(y_f – y₀),

where the initial height y₀ = 0, such that:

∆PE_grav = (0.012 kg)·(9.80 N/kg)·(+110×10³ m – 0) = 12,936 J,

or to two significant figures, 1.3×10⁴ J.

(Response (A) is (1/2)·m·g; response (B) is (1/2)·m·g·y_f; while response (D) is m·g·(y_f)².)

Student responses
Sections 30880, 30881
(A) : 2 students
(B) : 2 students
(C) : 39 students
(D) : 0 students

Success level: 90%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.25