Physics midterm problem: St. Lawrence River rocket car jump

Physics 205A Midterm 1, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 3.53

"Rocket Lincoln jump"

In 1979, a rocket-powered Lincoln Continental attempted to jump 1,600 m (approximately 1.0 mile) across the St. Lawrence River by traveling 120 m/s (approximately 270 mph) off the edge of a ramp angled 30° above the horizontal at a height of 30 m (approximately 100 ft) above the ground.[*] Three years earlier during the ramp construction process, stuntman Evel Knievel had reported for ABC's Wide World of Sports that this would not be feasible as designed. Determine whether Knievel's assessment was correct or incorrect. Neglect friction and drag. Show your work and explain your reasoning using properties of projectile motion.

[*] Robert Fortier, "The Devil At Your Heels," National Film Board of Canada (1981), onf.ca/film/devil_at_your_heels. (Last-minute substitute stuntman Kenny Powers survived the failed attempt.)

Solution and grading rubric:
  • p:
    Correct. Finds x- and y-components of initial velocity vector, then applies projectile motion equations in a methodical manner, and either:
    1. finds t when car reaches ground level (y = –30 m, assuming y0 = 0), and determines that the car would horizontally be located at x = v0xt, which is less than +1,600 m; or
    2. finds required t for car to travel to x = +1,600 m, and determines that the car would be below ground level at that time; and concludes that this jump is not feasible; or
    3. may also solve for time to reach highest point in trajectory, then doubles this time and finds that car would travel less than required x = +1,600 m, with implicit or explicit assumptions regarding the existence of a landing ramp of similar dimensions (y = 0, x = +1,600 from ramp edge to ramp edge), etc.
  • r:
    Nearly correct, but includes minor math errors.
  • 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 math errors notwithstanding.
  • v:
    Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at systematic use of kinematic equations for projectile motion.
  • x:
    Implementation of ideas, but credit given for effort rather than merit.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
Grading distribution:
Sections 70854, 70855
Exam code: midterm01sWFf
p: 14 students
r: 13 students
t: 8 students
v: 22 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1101), comparing the time for the car to travel 1,600 m horizontally to the predicted time of flight for the car until it reaches the ground. Note the alligator in the St. Lawrence River:

Another sample "p" response (from student 1408), calculating the time for the car to return to the launch height by multiplying the time to reach its highest height by two (thus supposing a landing ramp), and finding that the horizontal distance traveled would be less than 1,600 m:

Another sample "p" response (from student 1970), calculating the time for the car to travel 1,600 m horizontally, then determining that the car would need to be 238 m vertically below its starting height in order to travel that horizontal distance:

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