Physics final exam problem: more dangerous collision type

Physics 205A Final Exam, fall semester 2015
Cuesta College, San Luis Obispo, CA

A 2016 Fiat 500X car[*] (mass 1.2×10³ kg) driving at 2.0 m/s collides with a stationary Ford F-150 pick-up truck[**] (mass 1.8×10³ kg). It is claimed that an elastic collision is more dangerous for the passengers than a completely inelastic collision[***].

1. For an elastic collision, the car would rebound with a speed of 0.40 m/s in the reverse direction (while the truck would move forward after the collision).
2. For a completely inelastic collision between the car and truck, they would stick and both move together in the forward direction.

Solve for (a) the final speed of the truck after the elastic collision, (b) the final speed of the truck after the completely inelastic collision, and (c) discuss whether this claim is plausible or implausible. Ignore friction, drag, and external forces. Show your work and explain your reasoning using properties of collisions, energy (non-)conservation, and momentum conservation.

[*] caranddriver.com/fiat/500.
[**] buyersguide.caranddriver.com/ford/f-150/specs#features.
[***] James Cunningham, Norman Herr, Hands-On Physics Activities with Real-Life Applications: Easy-to-Use Labs and Demonstrations for Grades 8-12, Wiley (1994), p. 323.

Solution and grading rubric:

• p:
  Correct. Determines/discusses:
  1. the final velocity of the truck in the elastic collision from applying momentum conservation;
  2. the final velocity of the truck in the completely inelastic collision from applying momentum conservation; and
  3. makes some reasonable interpretation that the claim of the elastic collision being more dangerous than a completely inelastic collision is plausible, given that the initial-to-final velocity changes for the truck (and the car) are greater for the elastic collision than for the inelastic collision.
• r:
  Nearly correct, but includes minor math errors.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. At least has one correct final velocity for the truck, the other result is problematic but at least momentum conservation was applied.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying momentum conservation to find the final velocity of the truck for one collision, but the other collision is incomplete or conceptually problematic (such as applying kinetic energy conservation for the completely inelastic collision, claiming zero final velocities, etc.).
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach involving methods other than momentum conservation.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: final7rUk
p: 24 students
r: 3 students
t: 14 students
v: 16 students
x: 6 students
y: 5 students
z: 2 students

A sample "p" response (from student 1793):