Physics midterm problem: A-10 Thunderbolt II "Hawg-wash"

Physics 205A Midterm 2, fall semester 2015
Cuesta College, San Luis Obispo, CA

"30mm GAU 8 Avenger Impacts - Slowmo (IMAX Fighter Pilot Movie)"
XNeo27564
youtu.be/nk1HU5WShpU

The possible effect of recoil on an airplane is described[*] below:

Affectionately known as the "Hawg," the A-10 Thunderbolt II is essentially a flying gun designed to provide close air support to troops on the ground... An old rumor that a reader recently asked about is the A-10's gun is so powerful that when fired the recoil slows the plane down almost to a complete stop....
      The myth that its cannon drastically decelerates the aircraft is pure "Hawg-wash," said retired Air Force Col. Steve Ruehl. "I have fired as many as 500 rounds in one trigger burst..."

The mass of the aircraft[**] is 2.30×10⁴ kg, and the combined mass of 500 bullets[***] is approximately 200 kg. Assume that the aircraft (and bullets inside) are initially flying horizontally in the forward direction at a speed of 190 m/s, and then 500 bullets are fired all at the same time with a speed of 1,200 m/s out from the front of the aircraft (as measured by an outside observer). Ignore the effects of friction, drag, and the thrust of the aircraft engines (assuming that aircraft is just gliding) during the brief amount of time that the bullets were fired. Find (a) the final speed of the aircraft after firing 500 bullets (all at the same time); then (b) discuss whether the claim that "the recoil slows the plane down almost to a complete stop" is plausible. Show your work and explain your reasoning using properties of collisions, energy (non-)conservation, and momentum conservation.

[*] stripes.com/blogs/the-rumor-doctor/the-rumor-doctor-1.104348/does-the-a-10-s-gun-slow-the-plane-when-fired-1.152557.
[**] globalsecurity.org/military/systems/aircraft/a-10-specs.htm.
[***] orbitalatk.com/defense-systems/small-caliber-systems/30mm/docs/GAU-8A_Fact_Sheet.pdf.

Solution and grading rubric:

• p:
  Correct. Momentum is conserved as external impulses from drag and the aircraft engines are to be ignored, and:
  1. sets up momentum conservation for the aircraft and the bullets to solve for the final velocity of the aircraft;
  2. discusses implausibility of claim that the "recoil slows the plane down almost to a complete stop" from the very slight decrease in the speed of the aircraft.
• r:
  Nearly correct, but includes minor math errors in (1), or tangential/minor conceptual errors in (2).
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Certain parameters are misplaced or misidentified (typically sets initial velocity of bullets is zero), but at least successfully applied momentum conservation to find final velocity of aircraft, and discussion is consistent with result.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least some systematic attempt at using momentum conservation.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No clear attempt at applying momentum conservation.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm02h4W6
p: 33 students
r: 6 students
t: 3 students
v: 8 students
x: 5 students
y: 1 student
z: 0 students

A sample "p" response (from student 2060):