1
1. Vectors
Part A
What is the x component of [pic]?
Express your answer to two significant figures.
Top of Form
[pic] =2.50Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part B
What is the y component of [pic]?
Express your answer to the nearest integer.
Top of Form
[pic] =3.00Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part C
What is the y component of [pic]?
Express your answer to the nearest integer.
Top of Form
[pic] =−3.00Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part D
What is the [pic]component of [pic]?
Express your answer to the nearest integer.
Top of Form
[pic] =−2.00Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
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 [pic]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 [pic].
Express your answers to the nearest integer.
Top of Form
[pic], [pic] =2.00,−3.00Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part F
In ordered pair notation, write down the components of vector [pic].
Express your answers to the nearest integer.
Top of Form
[pic], [pic] =2.00,−3.00Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part G
What is true about [pic]and [pic]? Choose from the pulldown list below.
Top of Form
They are the same vectors.Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
2.2Part A
Which of the following procedures will add the vectors [pic]and [pic]?
Top of Form
Put the tail of [pic]on the arrow of [pic]; [pic]goes from the tail of [pic]to the arrow of [pic]
Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
It is equally valid to put the tail of [pic]on the arrow of [pic]; then [pic]goes from the tail of [pic]to the arrow of [pic].
Part B
Find [pic], the length of [pic], the sum of [pic]and [pic].
[pic]
Express [pic]in terms of [pic], [pic], and angle [pic].
Top of Form
[pic] =sqrt(A^2+B^2+2*A*B*cos(theta))Solution Requested
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part C
Find the angle [pic]that the vector [pic]makes with vector [pic].
Express [pic]in terms of [pic]and any of the quantities given in the problem introduction ( [pic], [pic], and/or [pic]) as well as any necessary constants. Use asin for arcsine
Top of Form
[pic] =asin((sin(pi-theta)*B)/C)Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
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 [pic]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.
Top of Form
falseCorrect
Bottom of Form
[pic][pic][pic][pic][pic][pic]
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 [pic]and its angle with respect to [pic], which of the following orientations simplifies the calculation the most?
Top of Form
The x axis should be oriented along [pic]
Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part F
Find the components of [pic]in the coordinate system shown.
[pic]
Express your answer as an ordered pair: x component, y component ; in terms of [pic]and [pic].
Top of Form
[pic] =B*cos(theta),B*sin(theta)Solution Requested
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part G
In the same coordinate system, what are the components of [pic]?
Express your answer as an ordered pair separated by a comma. Give your answer in terms of variables defined in the introduction ( [pic], [pic], and [pic]).
Top of Form
[pic] =A + B*cos(theta),B*sin(theta)Solution Requested
Bottom of Form
[pic][pic][pic][pic][pic][pic]
2.3Part A
Define the displacement of the plane while the radar was tracking it: [pic]. What are the components of [pic]?
Note: Use three significant figures in your intermediate calculations.
Express [pic]numerically as an ordered pair, separating the x and z components with a comma, to an accuracy of two significant figures.
Top of Form
[pic] =−1100,26.00 mSolution Requested
Bottom of Form
[pic][pic][pic][pic][pic][pic]
2.4Part A
Express [pic]as an ordered triplet of values, separated by commas.
Top of Form
[pic] =0,0,10.0Allowed attempts exceeded; answer displayed
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part B
Find the magnitude of [pic].
Top of Form
[pic] =10.0Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part C
Find the sine of the angle between [pic]and [pic].
Top of Form
[pic] =0.707Allowed attempts exceeded; answer displayed
Bottom of Form
[pic][pic][pic][pic][pic][pic]
2. One Dimensional Kinematics
Part A
The variable [pic]is, in general, a function of time.
Top of Form
trueCorrect
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part B
The variable [pic]is, in general, a function of time.
Top of Form
falseCorrect
Bottom of Form
[pic][pic][pic][pic][pic][pic]
The subscript on [pic]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 [pic]is, in general, a function of time.
Top of Form
falseCorrect
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part D
The variable [pic]is, in general, a function of time.
Top of Form
falseCorrect
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part E
The variable [pic]is, in general, a function of time.
Top of Form
trueCorrect
Bottom of Form
[pic][pic][pic][pic][pic][pic]
The velocity [pic]always varies with time when the acceleration is nonzero.
Part F
The variable [pic]is, in general, a function of time.
Top of Form
trueCorrect
Bottom of Form
[pic][pic][pic][pic][pic][pic]
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 [pic]is constant):
1. [pic],
2. [pic],
3. [pic].
Determine whether the following statements about the time variable [pic]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 [pic]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.
Top of Form
sometimesCorrect
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part H
The variable [pic]refers to the time interval between the moment when the moving object's position and velocity were [pic]and [pic]and the moment when the moving object's position and velocity are given by the formulas in the problem introduction.
Top of Form
alwaysCorrect
Bottom of Form
[pic][pic][pic][pic][pic][pic]
The "origin of time" is the time defined to be [pic]. 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 [pic]in these equations is always the time shown on your timer.
Top of Form
falseCorrect
Bottom of Form
[pic][pic][pic][pic][pic][pic]
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 [pic]and [pic]). In this case, the equations can be used as written. Otherwise, you will need to replace [pic]with [pic], where [pic]is the initial time as just defined. For example, if a problem involves two objects, one that starts accelerating at time [pic]and another that starts accelerating at some later time [pic], you would need to replace [pic]with [pic]in the equations of motion for the second object.
Part J
Which of the given equations is not an explicit function of [pic]and is therefore useful when you don't know or don't need the time?
Top of Form
[pic]Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
3.2Part A
Find the maximum height [pic]that the rocket reaches (neglecting air resistance).
Express the maximum height in terms of [pic], [pic], and/or [pic]. Note that in this problem, [pic]is a positive number equal to the magnitude of the acceleration due to gravity.
Top of Form
[pic] =0.5*a*t_1^2 + (0.5*a^2*t_1^2)/gSolution Requested
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part B
If the rocket's net acceleration is [pic]for [pic], what is the maximum height the rocket will reach?
Express your answer numerically in meters, using [pic].
Top of Form
[pic] =1470 mCorrect
Bottom of Form
[pic][pic][pic][pic][pic][pic]
3.3Part A
If the ball that is thrown downward has an acceleration of magnitude [pic]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 [pic]and [pic], the magnitude of the acceleration of gravity?
Top of Form
[pic]
Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part B
Which ball has the greater acceleration at the instant of release?
Top of Form
Neither; the accelerations of both balls are the same.Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part C
Which ball has the greater speed at the instant of release?
Top of Form
Neither; the speeds are the same.Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part D
Which ball has the greater average speed during the 1-s interval after release (assuming neither hits the ground during that time)?
Top of Form
the ball thrown downward
Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part E
Which ball hits the ground with greater speed?
Top of Form
Neither; the balls hit the ground with the same speed.Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
3.4
Part A
At what time(s) do the rockets have the same velocity?
Top of Form
at some instant in time between [pic]and [pic]
Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part B
At what time(s) do the rockets have the same x position?
Top of Form
at times [pic]and [pic]
Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part C
At what time(s) do the two rockets have the same acceleration?
Top of Form
at no time shown in the figureCorrect
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part D
The motion of the rocket labeled A is an example of motion with uniform (i.e., constant) __________.
Top of Form
and nonzero acceleration
Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part E
The motion of the rocket labeled B is an example of motion with uniform (i.e., constant) __________.
Top of Form
velocity
Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
Part F
At what time(s) is rocket A ahead of rocket B?
Top of Form
before [pic]and after [pic]
Correct
Bottom of Form
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 [pic]and [pic]
Top of Form
[pic] =v_0/a_0Solution Requested
Bottom of Form
[pic][pic][pic][pic][pic][pic]
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 [pic]and [pic].
Top of Form
[pic] =v_0/a_0Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
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 [pic]again?
Express the separation distance in terms of [pic]and [pic]. Your answer should be positive.
Top of Form
[pic] =(v_0^2)/a_0Solution Requested
Bottom of Form
[pic][pic][pic][pic][pic][pic]
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 [pic]and [pic]
Top of Form
[pic] =v_0/a_0Solution Requested
Bottom of Form
[pic][pic][pic][pic][pic][pic]
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 [pic]and [pic].
Top of Form
[pic] =v_0/a_0Correct
Bottom of Form
[pic][pic][pic][pic][pic][pic]
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 [pic]again?
Express the separation distance in terms of [pic]and [pic]. Your answer should be positive.
Top of Form
[pic] =(v_0^2)/a_0Solution Requested
Bottom of Form
[pic][pic][pic][pic][pic][pic]
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