Physics quiz question: downwards-aimed BB pellet vertical component

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. The initial vertical velocity component of the pellet was:
(A) –67 m/s.
(B) –80 m/s.
(C) –88 m/s.
(D) –1.4×10² m/s.

Correct answer (highlight to unhide): (A)

The initial velocity vector of the BB is 40° below the horizontal, which corresponds to an angle of θ = 360° – 40° = 320°, as measured counterclockwise from the +x axis (i.e., the "unit circle angle"). Using this θ = 320° 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 vertical component of the initial velocity vector is then:

v_0y = v₀·sinθ,

v_0y = (105 m/s)·sin(320°) = –67.4926990171 m/s,

or to two significant figures, v_0y = –67 m/s.

(Response (B) is (105 m/s)·cos(320°); response (C) is (105 m/s)·tan(320°); response (D) is (105 m/s)/cos(320°).)

Sections 70854, 70855, 73320
Exam code: quiz03sHO7
(A) : 30 students
(B) : 19 students
(C) : 7 students
(D) : 1 student

Success level: 53%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.61