Express Your Answer to Two Significant Figures

1. Vectors

Part A

What is the x component of ?

Express your answer to two significant figures.

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=2.50Correct

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Part B

What is the y component of ?

Express your answer to the nearest integer.

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=3.00Correct

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Part C

What is the y component of ?

Express your answer to the nearest integer.

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=−3.00Correct

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Part D

What is the component of ?

Express your answer to the nearest integer.

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=−2.00Correct

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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.

Part E

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

Express your answers to the nearest integer.

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, =2.00,−3.00Correct

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Part F

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

Express your answers to the nearest integer.

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, =2.00,−3.00Correct

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Part G

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

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They are the same vectors.Correct

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2.2Part A

Which of the following procedures will add the vectors and ?

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Put the tail of on the arrow of ; goes from the tail of to the arrow of
Correct

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It is equally valid to put the tail of on the arrow of ; then goes from the tail of to the arrow of .

Part B

Find , the length of , the sum of and .

Express in terms of , , and angle .

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=sqrt(A^2+B^2+2*A*B*cos(theta))Solution Requested

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Part C

Find the angle that the vector makes with vector .

Express in terms of and any of the quantities given in the problem introduction ( , , and/or ) as well as any necessary constants. Use asin for arcsine

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=asin((sin(pi-theta)*B)/C)Correct

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Addition using vector components

Part D

To manipulate these vectors using vector components, we must first choose a coordinate system. In this case choosing means specifying the angle of the x axis. The y axis must be perpendicular to this and by convention is oriented radians counterclockwise from the x axis.

Indicate whether the following statement is true or false:

There is only one unique coordinate system in which vector components can be added.

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falseCorrect

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Part E

The key point is that you are completely free to choose any coordinate system you want in which to manipulate the vectors. It is a matter of convenience only, and so you must consider which orientation will simplify finding the components of the given vectors and interpreting the results in that coordinate system to get the required answer. Considering these factors, and knowing that you are going to be required to find the length of and its angle with respect to , which of the following orientations simplifies the calculation the most?

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The x axis should be oriented along
Correct

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Part F

Find the components of in the coordinate system shown.

Express your answer as an ordered pair: x component, y component ; in terms of and .

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=B*cos(theta),B*sin(theta)Solution Requested

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Part G

In the same coordinate system, what are the components of ?

Express your answer as an ordered pair separated by a comma. Give your answer in terms of variables defined in the introduction ( , , and ).

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=A + B*cos(theta),B*sin(theta)Solution Requested

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2.3Part A

Define the displacement of the plane while the radar was tracking it: . What are the components of ?

Note: Use three significant figures in your intermediate calculations.

Express numerically as an ordered pair, separating the x and z components with a comma, to an accuracy of two significant figures.

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=−1100,26.00mSolution Requested

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2.4Part A

Express as an ordered triplet of values, separated by commas.

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=0,0,10.0Allowed attempts exceeded; answer displayed

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Part B

Find the magnitude of .

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=10.0Correct

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Part C

Find the sine of the angle between and .

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=0.707Allowed attempts exceeded; answer displayed

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2. One Dimensional Kinematics

Part A

The variable is, in general, a function of time.

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trueCorrect

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Part B

The variable is, in general, a function of time.

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falseCorrect

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The subscript on indicates that it is a fixed initial parameter, not a variable. It refers to the position of an object at some initial time.

Part C

The variable is, in general, a function of time.

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falseCorrect

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Part D

The variable is, in general, a function of time.

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falseCorrect

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Part E

The variable is, in general, a function of time.

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trueCorrect

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The velocity always varies with time when the acceleration is nonzero.

Part F

The variable is, in general, a function of time.

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trueCorrect

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It is best to write the kinematic equations for constant acceleration to show explicitly which variables are, in fact, functions of time (and to stress that is constant):

1. ,
2. ,
3. .

Determine whether the following statements about the time variable in the equations from the problem introduction are always, sometimes, or never true.

Again, be careful in answering; some of the wording will seem ambiguous or contorted until you understand what is being asked.

Part G

The variable refers to the time interval between the earliest event mentioned in the problem statement and the moment when the moving object's position and velocity are given by the formulas in the problem introduction.

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sometimesCorrect

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Part H

The variable refers to the time interval between the moment when the moving object's position and velocity were and and the moment when the moving object's position and velocity are given by the formulas in the problem introduction.

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alwaysCorrect

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The "origin of time" is the time defined to be . If you are using a wall clock as your timer, the origin of time would be noon or midnight. If you are using a calendar, the origin would be midnight on January 1st of Year 1. In a physics problem, the origin of time may or may not be specified.

Part I

Is the following statement true or false?

The moment chosen for the origin of time always cancels out and therefore the in these equations is always the time shown on your timer.

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falseCorrect

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Often it is possible to define the origin of time to be the same as the "initial time," the instant when the initial conditions are specified (i.e., so that and ). In this case, the equations can be used as written. Otherwise, you will need to replace with , where is the initial time as just defined. For example, if a problem involves two objects, one that starts accelerating at time and another that starts accelerating at some later time , you would need to replace with in the equations of motion for the second object.

Part J

Which of the given equations is not an explicit function of and is therefore useful when you don't know or don't need the time?

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Correct

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3.2Part A

Find the maximum height that the rocket reaches (neglecting air resistance).

Express the maximum height in terms of , , and/or . Note that in this problem, is a positive number equal to the magnitude of the acceleration due to gravity.

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=0.5*a*t_1^2 + (0.5*a^2*t_1^2)/gSolution Requested

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Part B

If the rocket's net acceleration is for , what is the maximum height the rocket will reach?

Express your answer numerically in meters, using .

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=1470mCorrect

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3.3Part A

If the ball that is thrown downward has an acceleration of magnitude at the instant of its release (i.e., when there is no longer any force on the ball due to the woman's hand), what is the relationship between and , the magnitude of the acceleration of gravity?

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Correct

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Part B

Which ball has the greater acceleration at the instant of release?

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Neither; the accelerations of both balls are the same.Correct

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Part C

Which ball has the greater speed at the instant of release?

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Neither; the speeds are the same.Correct

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Part D

Which ball has the greater average speed during the 1-s interval after release (assuming neither hits the ground during that time)?

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the ball thrown downward
Correct

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Part E

Which ball hits the ground with greater speed?

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Neither; the balls hit the ground with the same speed.Correct

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3.4

Part A

At what time(s) do the rockets have the same velocity?

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at some instant in time between and
Correct

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Part B

At what time(s) do the rockets have the same x position?

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at times and
Correct

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Part C

At what time(s) do the two rockets have the same acceleration?

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at no time shown in the figureCorrect

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Part D

The motion of the rocket labeled A is an example of motion with uniform (i.e., constant) ______.

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and nonzero acceleration
Correct

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Part E

The motion of the rocket labeled B is an example of motion with uniform (i.e., constant) ______.

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velocity
Correct

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Part F

At what time(s) is rocket A ahead of rocket B?

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before and after
Correct

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3.5

Part A

How much time does it take for the car to come to a full stop?

Express your answer in terms of and

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=v_0/a_0Solution Requested

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Part B

How much time does it take for the car to accelerate from the full stop to its original cruising speed?

Express your answer in terms of and .

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=v_0/a_0Correct

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Part C

The train does not stop at the stoplight. How far behind the train is the car when the car reaches its original speed again?

Express the separation distance in terms of and . Your answer should be positive.

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=(v_0^2)/a_0Solution Requested

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3.6

Part A

How much time does it take for the car to come to a full stop?

Express your answer in terms of and

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=v_0/a_0Solution Requested

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Part B

How much time does it take for the car to accelerate from the full stop to its original cruising speed?

Express your answer in terms of and .

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=v_0/a_0Correct

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Part C

The train does not stop at the stoplight. How far behind the train is the car when the car reaches its original speed again?

Express the separation distance in terms of and . Your answer should be positive.

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=(v_0^2)/a_0Solution Requested

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