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Adding scalar multiples of vectors graphically mastering physics

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10/6/2014 HW3


http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=3212823 1/21


HW3 Due: 11:59pm on Monday, October 13, 2014


To understand how points are awarded, read the Grading Policy for this assignment.


Tactics Box 3.3 Determining the Components of a Vector


Learning Goal:


To practice Tactics Box 3.3 Determining the component of a vector.


When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This Tactics Box describes how to determine the x component and y component of vector , denoted and .


TACTICS BOX 3.3 Determining the components of a vector


1. The absolute value of the x component is the magnitude of the component vector .


2. The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction.


3. The y component is determined similarly.


Part A


What is the magnitude of the component vector shown in the figure?


Express your answer in meters to two significant figures.


ANSWER:


Part B


What is the sign of the y component of vector shown in the figure?


A ⃗ A ⃗ x A ⃗ y


A ⃗ Ax Ay


| |Ax Ax A ⃗ x


Ax A ⃗ x A


⃗ x


Ay


A ⃗ x


= | |Ax m


Ay A ⃗


10/6/2014 HW3


http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=3212823 2/21


ANSWER:


Part C


This question will be shown after you complete previous question(s).


Components of Vectors


Shown is a 10 by 10 grid, with coordinate axes x and y . The grid runs from -5 to 5 on both axes. Drawn on this grid are four vectors, labeled through . This problem will ask you various questions about these vectors. All answers should be in decimal notation, unless otherwise specified.


Part A


What is the x component of ?


Express your answer to two significant figures.


positive negative


A ⃗ D⃗


A ⃗


10/6/2014 HW3


http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=3212823 3/21


You did not open hints for this part.


ANSWER:


Part B


What is the y component of ?


Express your answer to the nearest integer.


ANSWER:


Part C


What is the y component of ?


Express your answer to the nearest integer.


You did not open hints for this part.


ANSWER:


Part D


What is the component of ?


Express your answer to the nearest integer.


You did not open hints for this part.


ANSWER:


The following questions will ask you to give both components of vectors using the ordered pairs method. In this method, the x component is written first, followed by a comma, and then the y component. For example, the components of would be written 2.5,3 in ordered pair notation.


The answers below are all integers, so estimate the components to the nearest whole number.


= Ax


A ⃗


= Ay


B⃗


= By


x C ⃗


= Cx


A ⃗


10/6/2014 HW3


http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=3212823 4/21


Part E


In ordered pair notation, write down the components of vector .


Express your answers to the nearest integer.


ANSWER:


Part F


In ordered pair notation, write down the components of vector .


Express your answers to the nearest integer.


ANSWER:


Part G


What is true about and ? Choose from the pulldown list below.


ANSWER:


Problem 3.15


A wildlife researcher is tracking a flock of geese. The geese fly 4.5 due west, then turn toward the north by 50 and fly another 5.0 .


Part A


How far west are they of their initial position?


Express your answer to two significant figures and include the appropriate units.


ANSWER:


Part B


B⃗


, = Bx By


D⃗


, = Dx Dy


B⃗ D⃗


They have different components and are not the same vectors. They have the same components but are not the same vectors. They are the same vectors.


km ∘ km


= dw


10/6/2014 HW3


http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=3212823 5/21


What is the magnitude of their displacement?


Express your answer to two significant figures and include the appropriate units.


ANSWER:


Problem 3.5


A position vector with magnitude 20 points to the right and up. Its -component is 16 .


Part A


What is the value of its -component?


Express your answer to two significant figures and include the appropriate units.


ANSWER:


Problem 3.2


Part A


Draw the vector .


ANSWER:


= d


m x m


y


= y


= +C ⃗ A ⃗ B⃗


10/6/2014 HW3


http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=3212823 6/21


Part B


Draw the vector .


ANSWER:


= −D⃗ A ⃗ B⃗


10/6/2014 HW3


http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=3212823 7/21


Problem 3.1


Part A


Draw the vector .


ANSWER:


Part B


Draw the vector .


ANSWER:


= +D⃗ A ⃗ B⃗


= −C ⃗ A ⃗ B⃗


10/6/2014 HW3


http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=3212823 8/21


Vector Magnitude and Direction Conceptual Question


A man out walking his dog makes one complete pass around a perfectly square city block. He starts at point A and walks clockwise around the block.


Let be the displacement vector from A to B, be the displacement vector from B to C, etc.


Part A


Which of the following vectors is equal to ?


You did not open hints for this part.


r ⃗ AB r ⃗ BC


r ⃗ AB


10/6/2014 HW3


http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=3212823 9/21


ANSWER:


Part B


Which of the following vectors is equal to ?


ANSWER:


Part C


Which of the following vectors is equal to ?


You did not open hints for this part.


ANSWER:


Adding and Subtracting Vectors Conceptual Question


Six vectors (A to F) have the magnitudes and directions indicated in the figure.


only

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