{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

phyhw4 - valdez(vv689 – Homework 04 – florin –(58140...

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 Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: valdez (vv689) – 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 = 9 . 46 m, A y = 2 . 04 m, B x = 9 . 15 m, B y = − 4 . 14 m. Let R = A + B . Find the magnitude of R . Correct answer: 18 . 7281 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 = (9 . 46 m + 9 . 15 m) i + (2 . 04 m + ( − 4 . 14 m)) j = 18 . 61 m i + ( − 2 . 1 m) j . The magnitude, R , of R is R = radicalBig R 2 x + R 2 y = radicalBig (18 . 61 m) 2 + ( − 2 . 1 m) 2 = 18 . 7281 m . 002 (part 2 of 2) 10.0 points Find the angle θ 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: − 6 . 43817 ◦ . Explanation: The point is in the fourth quadrant of the coordinate system, so the angle θ that the vector R = A + B makes with the positive x axis is θ = arctan R y R x = arctan ( − 2 . 1 m) (18 . 61 m) = ( − 6 . 43817 ◦ ) = − 6 . 43817 ◦ . 003 (part 1 of 2) 10.0 points Consider two vectors vector A and vector B and their resul- tant vector A + vector B . The magnitudes of the vectors vector A and vector B are, respectively, 19 . 3 and 8 and they act at 130 ◦ to each other. vector A vector B vector A + vector B Find the magnitude of the resultant vector vector A + vector B . Correct answer: 15 . 4272. Explanation: Let : a = 19 . 3 , b = 8 , and θ = 130 ◦ . b γ r a γ = 180 ◦ − 130 ◦ = 50 ◦ , so applying the law of cosines, r 2 = a 2 + b 2 − 2 a b cos γ = (19 . 3) 2 + (8) 2 − 2 (19 . 3) (8) cos 50 ◦ = 237 . 997 r = √ 237 . 997 = 15 . 4272 . 004 (part 2 of 2) 10.0 points Find the angle between the direction of the resultant vector A + B and the direction of the vector A . Correct answer: 23 . 406 ◦ . valdez (vv689) – Homework 04 – florin – (58140) 2 Explanation: a r β γ b Applying the law of sines, b sin β = r sin γ sin β = b sin γ r β = arcsin parenleftbigg b sin γ r parenrightbigg = arcsin parenleftbigg 8 sin 50 ◦ 15 . 4272 parenrightbigg = 23 . 406 ◦ ....
View Full Document

{[ snackBarMessage ]}

Page1 / 7

phyhw4 - valdez(vv689 – Homework 04 – florin –(58140...

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

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