Physics final exam problem: EMAS (Engineered Material Arresting System) stopping distance of Boeing 727

Physics 205A Final Exam, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 2.63(a)

"EMAS - Engineered Material Arresting System"
defesanet
youtu.be/f9UWsB5lJ7M

The Federal Aviation Administration (FAA) tested a runway material that would slow airplanes to a stop in emergency situations where they would go past the end of a runway.[*]

Without use of brakes, or reverse thrust an FAA Boeing 727 [mass of 95,000 kg][**] overran the runaway at 28 m/s. The aircraft came to a full stop in 80 m, with passengers [inside the plane] only exposed to roughly 1 "g" [10 m/s²] deceleration. The computer model accurately predicted the performance of the final outcome within [six percent].

Determine whether or not the 1 "g" claim for the magnitude of the plane's acceleration is within a 6% error of its actual value. Show your work and explain your reasoning using properties of constant acceleration motion along the horizontal direction.

[*] defesanet, "EMAS - Engineered Material Arresting System," youtu.be/f9UWsB5lJ7M.
[**] "Boeing 727," wki.pe/Boeing_727#727-200.

Solution and grading rubric:

• p:
  Correct. With given values for the initial and final speeds, displacement, and magnitude of acceleration, uses three of these parameters to solve for the fourth parameter and compares to the given value, and finds that it is discrepant by a factor of two, which is inconsistent with the "accurately predicted the performance of the final outcome within [six percent]."
• r:
  Nearly correct, but includes minor math errors. Does not sufficiently compare discrepancy between calculated and given value in terms of the 6% uncertainty.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. At least some attempt at setting up kinematic equations of constant acceleration motion.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No clear attempt at applying kinematic equations of constant acceleration motion.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: finalm34T
p: 29 students
r: 13 students
t: 8 students
v: 7 students
x: 2 students
y: 2 students
z: 1 student

A sample "p" response (from student 1220), comparing the claimed and actual stopping distances:
Another sample "p" response (from student 6584), comparing the claimed and actual acceleration:
Yet another sample "p" response (from student 6674), using the work-energy theorem: