Physics midterm problem: Snake River Canyon rocket jump

Physics 205A Midterm 1, fall semester 2016
Cuesta College, San Luis Obispo, CA

"Stuntman successfully jumps Snake River Canyon"
KTVB Channel 7
ktvb.com/news/stuntman-successfully-jumps-snake-river-canyon/319488060

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:

• p:
  Correct. Discusses/demonstrates:
  1. given maximum height y = +670 m at x = +740 m, calculates the initial speed (or initial velocity components);
  2. compares calculated initial speed (or initial velocity components) with reported value, and concludes there is a discrepancy of more than two significant figures.
  May instead discuss/demonstrate:
  1. 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 v_y at y = +670 m, etc.;
  2. 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."
• r:
  Nearly correct, but includes minor math errors. At least successfully solves for the horizontal v_0x and vertical v_0y 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.
• t:
  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.
• 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, 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: