Physics quiz question: component of vector, given magnitude and other component

Physics 205A Quiz 3, fall semester 2015
Cuesta College, San Luis Obispo, CA

A vector R has a magnitude of 16 m, with a y-component R_y = –5.5 m. 
The x-component R_x is positive. The magnitude of the x-component R_x is:
(A) 3 m.
(B) 5 m.
(C) 15 m.
(D) 17 m.

Correct answer (highlight to unhide): (C)

The magnitude of vector R is the square root of the sum of the squares of its components:

|R| = sqrt(R_x² + R_y²),

such that the R_x can be solved for in terms of the magnitude |R| and y-component R_y:

|R|² = R_x² + R_y²,

|R|² – R_y² = R_x²,

sqrt(|R|² – R_y²) = R_x,

sqrt((16 m)² – (–5.5 m)²) = R_x,

such that (the magnitude of) R_x is 15 m.

Sections 70854, 70855, 73320
Exam code: quiz03re3T
(A) : 3 students
(B) : 1 student
(C) : 68 students
(D) : 2 students

Success level: 80%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.81