Physics midterm problem: thrown rock impact

Physics 8A Midterm 1, Fall Semester 2006
Cuesta College, San Luis Obispo, CA

Physics 8A learning goal Q3.4

[20 points.] A Physics 8A student stands on the roof of a building and throws a rock with a velocity of magnitude 20.0 m/s at an angle of 58.0 degrees above the horizontal, which is released at a height of 25.0 m above the ground. Ignore air resistance. Determine the magnitude (in m/s) and direction (with respect to the horizontal) of the velocity of the rock just as it strikes the ground. Show your work and explain your reasoning.

(Cf. Young and Freeman, University Physics, 11/e, Exercise 3.23.)

Solution and grading rubric:

• p = 20/20:
  Correct. Breaks v_0 into v_0x and v_0y. Since a_x = 0, then v_x = v_0x. Either uses the quadratic formula to solve for t, and then plugs in t to find v_y, or uses the "time-eliminated" equation to immediately solve for v_y. Finds magnitude of v (29.8 m/s) using the Pythagorean theorem, and the direction (–69.2 degrees or +291 degrees) using inverse tangent.
  
• r = 16/20:
  Nearly correct, but includes minor math errors.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least finds v_y, and/or time t.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Progress made in isolating unknowns in the kinematic equations of motion.
  
• x = 4/20:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
p: 13 students
r: 3 students
t: 6 students
v: 8 students
x: 4 students
y: 0 students
z: 0 students