Physics midterm problem: Washington Monument baseball catch

Physics 205A Midterm 1, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 3.47

Baseball player Charles "Gabby" Street, a catcher for the Washington Senators, was reported to have caught a baseball thrown from a window near the top of the Washington Monument on August 21, 1908 [*]. Assume that the baseball was initially thrown horizontally, and was caught at a horizontal distance of 6.0 m and a vertical distance of 160 m below from where it was thrown. What was the initial (horizontal) speed of the ball? Neglect air resistance. Show your and explain your reasoning using properties of projectile motion.

[*] Francis Stann, "Street's Ironic Monument," Baseball Digest, vol. 10, no. 4 (April 1951), pp. 29-30.

Solution and grading rubric:

• p:
  Correct. Determines the time t = 5.7 s for the baseball to fall (with no initial vertical velocity), and then solves for the initial horizontal velocity v_0x = x/t = 1.1 m/s. May either directly solve for t, or other equation(s) to first solve for the final vertical velocity v_y = –56 m/s.
  
• r:
  Nearly correct, but includes minor math errors. Uses quadratic equation coefficient a = –9.80 m/s² instead of –4.90 m/s², or x instead of y, or sets v_x = 0.
  
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Can at least solve for t or v_y.
  
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at systematic use of kinematic equations for projectile motion.
  
• x:
  Implementation of ideas, but credit given for effort rather than merit. Use of angular kinematic equations, etc.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: midterm01w4Sh
p: 35 students
r: 7 students
t: 2 students
v: 8 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 1123), solving for the final vertical velocity before ∆t:
Another sample "p" response (from student 3737), directly solving first for ∆t, with the additional baseball skills assessment of the person who released the ball from the Washington Monument: