Physics quiz question: Skycycle X-2 average speed vs. magnitude of average velocity

Physics 205A Quiz 3, fall semester 2017
Cuesta College, San Luis Obispo, CA

"Evel Knievel's Skycycle"
Tennessee Dept. of Tourism

Evel Knievel's Skycycle X-2 rocket ship was launched with an initial speed of 44 m/s at an angle of 56° above the horizontal[*]. Neglect air resistance, and treat the rocket as a thrown object. From being launched to reaching the highest height of its trajectory, the rocket ship's average speed will be __________ the magnitude of its average velocity.
(A) less than.
(B) equal to.
(C) greater than.
(D) (Not enough information is given.)

[*] James Vlahos, "The Devils And The Deep Blue Sky," popsci.com/article/technology/devils-and-deep-blue-sky, (September 24, 2014).

Correct answer (highlight to unhide): (C)

The average speed of the rocket ship is its distance traveled divided by elapsed time, while the magnitude of average velocity is given by the magnitude of displacement divided by elapsed time. For projectile motion, the distance traveled is measured along its curved trajectory, and is longer than the magnitude of the displacement, which is the length of the straight-line vector that starts from the ground, and ends at the highest point of its trajectory. Since the elapsed time for the rocket ship to travel from the start to finish is the same whether along the actual distance traveled or the straight-line displacement, the average speed of the rocket ship must be greater than the magnitude of its average velocity.

(Response (A) can never be true for any possible path taken by an object. Response (B) can only be true for an object traveling along a straight-line with no reversals in direction.)

Sections 70854, 70855
Exam code: quiz03T4uC
(A) : 6 students
(B) : 10 students
(C) : 32 students
(D) : 0 students

Success level: 59%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.63

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