Cuesta College, San Luis Obispo, CA
KTVB Channel 7
Stuntman Eddie Braun successfully completed a rocket jump over the Snake River in Idaho[*]. With a reported launch speed of 190 m/s at an angle of 55° above the horizontal, after traveling a horizontal distance of 740 m, the rocket reached a maximum height of 670 m above the ground.
Determine whether the reported 190 m/s was a plausible value for the launch speed (to within two significant figures). Neglect air resistance and the propulsion engine of the rocket (thus treating it as a thrown object). Show your work and explain your reasoning using properties of projectile motion.
[*] Loz Blain, "Eddie Braun Jumps the Snake River Canyon in an Evel Knievel-style Rocket Bike" (September 16, 2016), newatlas.com/eddie-braun-rocket-bike-jump-snake-river-knievel/45477/.
Solution and grading rubric:
- given maximum height y = +670 m at x = +740 m, calculates the initial speed (or initial velocity components);
- compares calculated initial speed (or initial velocity components) with reported value, and concludes there is a discrepancy of more than two significant figures.
- holding other given values as fixed to find some other inconsistency in a reported value, such as time t to reach y = +670 m, time t to reach x = +740 m, or looks for a non-zero vertical velocity component vy at y = +670 m, etc.;
- interprets that reported initial speed of 190 m/s is plausible in that the rocket jump would exceed the reported trajectory parameters and be "successful."
Nearly correct, but includes minor math errors. At least successfully solves for the horizontal v0x and vertical v0y components of the initial velocity vector, but calculation and/or conclusion from finding/deducing a derived value to compare to a reported value is garbled.
Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least enough steps are shown that would theoretically result in a complete answer, multiple errors notwithstanding.
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
Implementation of ideas, but credit given for effort rather than merit.
Irrelevant discussion/effectively blank.
Sections 70854, 70855, 73320
Exam code: midterm01br1Q
p: 29 students
r: 9 students
t: 6 students
v: 9 students
x: 3 students
y: 1 student
z: 0 students
A sample "p" response (from student 8321), finding that the reported initial velocity would result in a trajectory that would be higher and longer than the state values, and concludes that it is a plausible value in the sense that it would outdistance the (assumed) required trajectory:
Another sample "p" response (from student 3575), demonstrating that after the rocket has traveled a horizontal distance of 740 m, it is at a higher height than the stated maximum height of 670 m, and concludes that the reported initial velocity is a plausible value in that air resistance was not included in this analysis:
Yet another sample "p" response (from student 4566), showing a discrepancy in the vertical initial velocity component required in order for the rocket to reach its highest height of 670 m after traveling a horizontal distance of 740 m: