Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 3.37
From the edge of the rooftop of a building, a Physics 205A student throws a ball with an initial speed of 15.5 m/s at angle of 40.0° above the horizontal. Find (a) the maximum height of the ball as measured from the point from which it was thrown, and (b) the time that the ball reaches its maximum height. Neglect air resistance. Show your work and explain your reasoning.
Solution and grading rubric:
- p:
Correct. Finds x- and y-components of initial velocity: v0x = +11.9 m/s, v0y = +9.96 m/s. First solves for either the t or y of the highest point, and uses this to solve for the remaining unknown. - r:
Nearly correct, but includes minor math errors. - t:
Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least has t or y correct, has problems finding the remaining unknown. - v:
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. - x:
Implementation of ideas, but credit given for effort rather than merit. - y:
Irrelevant discussion/effectively blank. - z:
Blank.
Grading distribution:
Sections 70854, 70855
p: 19 students
r: 3 students
t: 5 students
v: 17 students
x: 1 student
y: 0 students
z: 0 students
A sample of a "p" response, solving for the time that the vertical velocity would be zero, and then using that time to solve for the vertical displacement (from student 0818):
Another "p" response (from student 1336), solving for the displacement when the vertical velocity is zero, and the going back and solving for the time:
Yet another "p" response (from student 7175), where the time when the displacement is zero is solved for, and halved to find the time of the highest point, which is then used to solve for the maximum vertical displacement:
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