Physics quiz question: "superhero landing" impulse

Physics 205A Quiz 4, fall semester 2019
Cuesta College, San Luis Obispo, CA

"Deadpool | 'Superhero Landing' | Official HD Clip 2016"
20th Century Fox UK
youtu.be/EwUilIo036g

In the movie Deadpool (2016), Angel Dust (portrayed by Gina Carano, mass 66 kg[*]) falls vertically downwards for a "superhero landing," coming to a complete stop from a downwards speed of 34 m/s in 0.24 s as she contacts the ground[**]. Ignore friction and drag. The magnitude of the stopping impulse of the ground on her was:
(A) 0 N·s.
(B) 2.2×10³ N·s.
(C) 9.4×10³ N·s.
(D) 3.8×10⁴ N·s.

[*] imdb.com/name/nm2442289/.
[**] Assuming an initial vertical speed of zero as she steps off the edge of a derelict helicarrier, with a flight deck assumed to be 60 m high above the ground.

Correct answer (highlight to unhide): (B)

From the impulse-momentum theorem, the impulse J on an object causes its initial-to-final change in momentum ∆p:

J = ∆p,

where ∆p = m·(v_f – v₀).

The initial velocity vector is v₀ = –34 m/s (traveling downwards), and the final velocity vector is v_f = 0 m/s ("a complete stop"). Then:

J = (66 kg)·((0 m/s) – (–34 m/s)) = (66 kg)·(+34 m/s) = +2,244 N·s,

or to two significant figures, the magnitude of the impulse is 2.2×10³ N·s (and the "+" sign indicates that it is in the upwards direction).

(Response (C) is the magnitude of the average stopping force over the 0.24 s stopping time interval; response (D) is the amount of translational kinetic energy dissipated by the landing.)

Sections 70854, 70855
Exam code: quiz04JuR4
(A) : 1 student
(B) : 27 students
(C) : 20 students
(D) : 4 students

Success level: 52%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.73