Physics final exam question: darts shot vertically from toy guns

Physics 205A Final Exam, fall semester 2016
Cuesta College, San Luis Obispo, CA

A 2008 NERF® N-Strike Recon CS-6 toy gun[*] can be modeled as a compressed spring that is released to launch a standard 1.3×10^–3 kg foam dart vertically from rest, to reach a maximum height of 13 m. A slightly more massive dart[**] is launched from rest from the same gun. Discuss why the more massive dart will reach a lower maximum height than the standard dart. Ignore drag/friction. Explain your reasoning using the properties of energy forms and (non-)conservation of energy.

[*] nerfhaven.com/forums/topic/23927-dart-mass-listing/.
[**] nerfguns.net/mods/mod-kits/.

Solution and grading rubric:

• p:
  Correct. Understands that:
  1. by setting up an energy/transfer equation (where there is no external work done by the environment) for the initial-to-final process of a stationary dart held against a loaded spring reaching its maximum height, the decrease in elastic potential energy is equal to the increase in gravitational potential energy; and
  the amount of elastic potential energy is the same for the standard or heavier dart, so the gravitational potential energy of the standard and heavier dart is the same when at their maximum heights; such that
  the standard dart will have a higher maximum height, while the heavier dart will have a lower maximum height, due to the difference in their masses.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May instead have a complete, correct argument using Newton's laws and kinematics rather than the requested use of energy forms and conservation.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. (Or minor inconsistencies/loopholes in Newton's laws and kinematics approach.)
• 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 energy changes and work.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. No clear attempt at applying energy changes and work.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855, 73320
Exam code: finali0w4
p: 18 students
r: 12 students
t: 18 students
v: 0 students
x: 0 students
y: 0 students
z: 1 student

A sample "p" response (from student):