Physics final exam problem: diagonally downwards-shoved ball

Physics 205A Final Exam, spring semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 3.96

A ball is shoved off the edge of a cliff with an initial velocity of 15 m/s at angle of 60° below the horizontal. How long does it take for the ball to fall to the ground 40 m below? Neglect air resistance. Show your work and explain your reasoning using properties of projectile motion.

Solution and grading rubric:

• p:
  Correct. Finds x- and y-components of initial velocity: v_0x = +7.50 m/s, v_0y = –13.0 m/s; and uses kinematic equations for constant acceleration to solve for t = 1.82 s, implementing the quadratic equation directly, or by first finding the final vertical velocity v_y, and then solving for t.
  
• r:
  Nearly correct, but includes minor math errors. May also have drawn the initial velocity vector as being 30° below the horizontal.
  
• 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. Some systematic attempt at resolving vectors into components, or using kinematics.
  
• x:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Sections 30880, 30881
p: 13 students
r: 9 students
t: 8 students
v: 7 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 0506):
Another sample "p" response (from student 1697):
A sample "r" response (from student 3693), with a sign error for the magnitude of vertical acceleration: