Physics quiz question: projectile motion average speed, magnitude of average velocity

Physics 205A Quiz 3, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 3.55(c)

A ball is thrown at a downwards angle from the edge of the rooftop of a building. The initial velocity vector has x- and y-components v_ix = –7.8 m/s, v_iy = –7.8 m/s. The ball hits the ground 0.80 s later. As the ball travels from the edge of the rooftop to the ground, which is the greater quantity?
(A) Average speed.
(B) Magnitude of average velocity.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer: (A)

Comparing average speed and magnitude of average velocity:

average speed = (distance traveled)/(time elapsed ∆t)),

magnitude of average velocity |v_av| = |displacement|/(time elapsed ∆t).

Since the ball undergoes projectile motion, the distance traveled would be measured along a parabolic trajectory, which would be longer than the magnitude of the displacement, which is the straight-line vector from the initial position (rooftop) to the final position (ground). Thus as the ball travels from the edge of the rooftop to the ground, the average speed would be greater than the magnitude of the average velocity.

Sections 70854, 70855
Exam code: quiz03sQr7
(A) : 17 students
(B) : 17 students
(C) : 31 students
(D) : 0 students

Success level: 31%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.86