Physics quiz question: BB pellet average speed vs. magnitude of average velocity

Physics 205A Quiz 3, fall semester 2016
Cuesta College, San Luis Obispo, CA

A BB gun shoots a pellet with a speed of 105 m/s at an angle of 40° below the horizontal, down towards the ground below. Neglect air resistance. After being shot out of the gun, but just before it hits the ground below, the pellet's average speed was __________ the magnitude of its average velocity.
(A) less than.
(B) equal to.
(C) greater than.
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (C)

The average speed of the BB 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 muzzle of the BB gun, and ends where the BB hits the ground. Since the elapsed time for the BB 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 BB 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, 73320
Exam code: quiz03sHO7
(A) : 8 students
(B) : 35 students
(C) : 14 students
(D) : 0 students

Success level: 25%
Discrimination index (Aubrecht & Aubrecht, 1983): –0.01

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