Physics final exam problem: diagonally downwards-thrown ball

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

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 3.62(c)

A ball is thrown off the edge of a vertical 29.0 m high cliff at an initial velocity of 17.0 m/s at angle of 45.0° below the horizontal. What horizontal distance from the bottom of the cliff does the ball land on the ground? Show your work and explain your reasoning.

Solution and grading rubric:

• p:
  Correct. Finds x- and y-components of initial velocity: v_0x = +12.0 m/s, v_0y = –12.0 m/s; and uses kinematic equations for constant acceleration along the vertical direction (i.e., free fall) to solve for t = 1.50 s, then finding the final position x = v_0x·t = +18.0 m.
  
• r:
  Nearly correct, but includes minor math errors. Also may have the initial velocity vector being 45° above the horizontal, but otherwise ha correct resulting horizontal distance.
  
• 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. Use of trigonometric relations to find horizontal distance.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Section 72177
p: 4 students
r: 1 student
t: 5 students
v: 1 student
x: 0 students
y: 1 student
z: 0 students

Sections 70854, 70855
p: 10 students
r: 10 students
t: 19 students
v: 8 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 2889), finding elapsed time from the quadratic formula, then solving for horizontal displacement:
Another sample "p" response (from student 7676) avoiding use of the quadratic formula by solving for the final vertical velocity (given the initial vertical velocity and vertical displacement), then finding the elapsed time for the horizontal displacement:
A sample "r" response (from student 8128), for a ball thrown at an angle of 45° above the horizontal:
A sample "v" response (from student 1407), using trigonometry to solve for the horizontal displacement of the ball, and also mixing velocity and displacement quantities in a 45°-45°-90° triangle: