20091015

Physics midterm problem: jumping frog

Physics 205A Midterm 1, fall semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 3.55(b)

[20 points.] A frog jumps at an angle of 40° from the horizontal, and lands back on the level ground 0.87 s later, a distance of 4.4 m away. Solve for the x- and y-components of its initial velocity. Show your work and explain your reasoning.

Solution and grading rubric:
  • p = 20/20:
    Correct. Solves for average horizontal speed from given horizontal displacement and elapsed time, this must also be the initial horizontal velocity component vix. Then can use the initial trajectory angle to solve for viy = vix·tan(40°). Or can use half of flight time, and vfy = 0 at top of trajectory to find viy .
  • r = 16/20:
    Nearly correct, but includes minor math errors. May have shifted a decimal place, or used tan(40°) = adjacent/opposite, or apparent miscalculation of otherwise correct equations.
  • t = 12/20:
    Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least has vix = ∆x/∆t. Garbles attempt at using kinematics to find viy (typically using 0.87 s as the time to travel to its highest height).
  • v = 8/20:
    Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Still has a methodical approach based on kinematics and/or trigonometry. May claim that ∆x/∆t is the magnitude of the initial velocity vector, which is then broken into vix and viy components using cos(40°) and sin(40°).
  • 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:
Sections 70854, 70855, 72177
p: 26 students
r: 9 students
t: 9 students
v: 9 students
x: 10 students
y: 2 students
z: 0 students

A sample of a "p" response, using the time of flight and initial velocity vector angle to solve for the magnitude of the initial velocity vector, which is then broken into x- and y- components (from student 2323):
Another "p" response, using the time of flight and the horizontal range to solve for the x-component of the initial velocity vector, and together with the initial velocity vector direction is used to find the y-component of the initial velocity vector (from student 6405):
An "r" response, but with the entire flight time used to find the y-component of the initial velocity vector (from student 1251):
Another "r" response, with a misapplication of the tangent function (from student 2051):
A sample of a "v" response, where the x-component of the initial velocity vector is used as the magnitude of the initial velocity vector (from student 9685):

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