Physics midterm problem: momentum comparison of slingshot ball and .44 Magnum bullet

Physics 205A Midterm 2, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Example 6.11, Conceptual Question 7.10

"Can a slingshot hit harder than handguns? The Shootout"
The Slingshot Channel
youtu.be/tLxnNP-ycVQ

Jörg Sprave from "The Slingshot Channel" made the following claim:

Mathematics say that this slingshot (with a 0.0681 kg ball) will have more momentum than most guns, except for this .44 Magnum[*].

Given that Jörg Sprave is able to stretch the slingshot's rubber bands (spring constant k = 110 N/m) by 1.60 m in a "butterfly draw"[*],[**], 
and that a .44 Magnum bullet[***] has a mass of 0.013 kg, and muzzle velocity of 391 m/s, determine whether this claim is plausible or not. Neglect friction and drag. Show your work and explain your reasoning.

[*] youtu.be/tLxnNP-ycVQ.
[**] youtu.be/kUvm6az46bg.
[***] "Bullet weight/type: 200 gr (13 g) JHP; Velocity: 1,282 ft/s (391 m/s)," wki.pe/.44_Magnum.

Solution and grading rubric:

• p:
  Correct. Applies (1) mechanical energy conservation to find final velocity of slingshot ball, to (2) calculate momentum of slingshot ball, and (3) calculates momentum of the .44 Magnum bullet to compare it to.
• r:
  Nearly correct, but includes minor math errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Successfully finds (3), but garbles attempt at (1). Or successfully finds (1), but compares speed of slingshot ball directly to bullet instead of comparing their momenta.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some constructive attempt at applying energy conservation and momentum calculations.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Minimal attempt at applying energy conservation and momentum calculations.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm02j0R6
p: 12 students
r: 10 students
t: 19 students
v: 20 students
x: 5 students
y: 1 student
z: 0 students

A sample "p" response (from student 9880):