hw5 - lavallo (jhl936) Homework 04 florin (58140) 1 This...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: lavallo (jhl936) Homework 04 florin (58140) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 2) 10.0 points Two vectors A and B , are lying in the xy plane and given by A = A x i + A y j B = B x i + B y j . where A x = 2 . 67 m, A y = 0 . 979 m, B x = 4 . 2 m, B y = 8 . 58 m. Let R = A + B . Find the magnitude of R . Correct answer: 10 . 2456 m. Explanation: The resultant vector R is given by R = A + B = ( A x i + A y j ) + ( B x i + B y j ) = ( A x + B x ) i + ( A y + B y ) j = (2 . 67 m + 4 . 2 m) i + (0 . 979 m + ( 8 . 58 m)) j = 6 . 87 m i + ( 7 . 601 m) j . The magnitude, R , of R is R = radicalBig R 2 x + R 2 y = radicalBig (6 . 87 m) 2 + ( 7 . 601 m) 2 = 10 . 2456 m . 002 (part 2 of 2) 10.0 points Find the angle that the vector R makes from the positive x axis. Choose your answer to be between 180 and +180 . The positive an- gular direction is counter clockwise measured from the x axis. Correct answer: 47 . 8918 . Explanation: The point is in the fourth quadrant of the coordinate system, so the angle that the vector R = A + B makes with the positive x axis is = arctan R y R x = arctan ( 7 . 601 m) (6 . 87 m) = ( 47 . 8918 ) = 47 . 8918 . 003 (part 1 of 2) 10.0 points Consider two vectors vector A and vector B and their re- sultant vector A + vector B . The magnitudes of the vectors vector A and vector B are, respectively, 14 . 5 and 6 . 1 and they act at 65 to each other. vector A vector B vector A + vector B Find the magnitude of the resultant vector vector A + vector B . Correct answer: 17 . 9505. Explanation: Let : a = 14 . 5 , b = 6 . 1 , and = 65 . b r a = 180 65 = 115 , so applying the law of cosines, r 2 = a 2 + b 2 2 a b cos = (14 . 5) 2 + (6 . 1) 2 2 (14 . 5) (6 . 1) cos 115 = 322 . 221 r = 322 . 221 = 17 . 9505 . 004 (part 2 of 2) 10.0 points Find the angle between the direction of the lavallo (jhl936) Homework 04 florin (58140) 2 resultant vector A + B and the direction of the vector A . Correct answer: 17 . 9378 . Explanation: a r b Applying the law of sines, b sin = r sin sin = b sin r = arcsin parenleftbigg b sin r parenrightbigg = arcsin parenleftbigg 6 . 1 sin 115 17 . 9505 parenrightbigg = 17 . 9378 ....
View Full Document

This note was uploaded on 04/09/2010 for the course PHY 58150 taught by Professor Florin during the Spring '10 term at University of Texas at Austin.

Page1 / 7

hw5 - lavallo (jhl936) Homework 04 florin (58140) 1 This...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online