20151003

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 Ry = –5.5 m. 
The x-component Rx is positive. The magnitude of the x-component Rx 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(Rx2 + Ry2),

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

|R|2 = Rx2 + Ry2,

|R|2Ry2 = Rx2,

sqrt(|R|2Ry2) = Rx,

sqrt((16 m)2 – (–5.5 m)2) = Rx,

such that (the magnitude of) Rx 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

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