Physics quiz question: soccer ball horizontal velocity component

Physics 205A Quiz 3, fall semester 2018
Cuesta College, San Luis Obispo, CA

A Physics 205A student kicks a soccer ball such 
that it has an initial speed of 21 m/s, with an angle of 155°, as measured counterclockwise from the +x direction. Neglect air resistance. The horizontal component of the soccer ball's initial velocity vector is:
(A) –19 m/s.
(B) –8.8 m/s.
(C) +8.8 m/s.
(D) +19 m/s.

Correct answer (highlight to unhide): (A)

The initial velocity vector of the soccer ball is at an angle of 155° as measured counterclockwise from the +x axis (i.e., the "unit circle angle"). Using this θ = 155° angle allows the ± signs in the initial velocity vector components to naturally result from the calculations:

v_0x = v₀·cosθ,
v_0y = v₀·sinθ.

Then the horizontal component of the initial velocity vector is then:

v_0x = v₀·cosθ,

v_0x = (21 m/s)·cos(155°) = –19.032463527769649 m/s,

or to two significant figures, v_0y = –19 m/s.

(Response (D) is the initial horizontal speed, but directed to the right; response (C) is the vertical component of the initial velocity vector (21 m/s)·sin(155°); response (D) is the initial vertical speed, but directed downwards.)

Sections 70854, 70855
Exam code: quiz03pRH5
(A) : 42 students
(B) : 5 students
(C) : 3 students
(D) : 6 students

Success level: 75%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.60