notation integers

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1. Vectors
Part A
What is the x component of ?
Express your answer to two significant figures.
=2.50Correct
Part B
What is the y component of ?
Express your answer to the nearest integer.
=3.00Correct
Part C
What is the y component of ?
Express your answer to the nearest integer.
=−3.00Correct
Part D
What is the component of ?
Express your answer to the nearest integer.
=−2.00Correct
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
2.5,3 in ordered pair notation.
would be written
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.
.
,
=2.00,−3.00Correct
Part F
In ordered pair notation, write down the components of vector
Express your answers to the nearest integer.
,
.
=2.00,−3.00Correct
Part G
What is true about and ? Choose from the pulldown list below.
They are the same vectors.Correct
2.2Part A
Which of the following procedures will add the vectors
Put the tail of
Correct
on the arrow of
;
goes from the tail of
and
?
to the arrow of
It is equally valid to put the tail of
the arrow of
Part B
Find
; then
goes from the tail of
to
.
, the length of
Express
on the arrow of
in terms of
, the sum of
,
and
.
, and angle .
=sqrt(A^2+B^2+2*A*B*cos(theta))Solution Requested
Part C
Find the angle that the vector
Express in terms of
makes with vector
.
and any of the quantities given in the problem introduction (
,
, and/or ) as well as any necessary constants. Use asin for arcsine
=asin((sin(pi-theta)*B)/C)Correct
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
x axis.
radians counterclockwise from the
Indicate whether the following statement is true or false:
There is only one unique coordinate system in which vector components can be added.
falseCorrect
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
angle with respect to
most?
and its
, which of the following orientations simplifies the calculation the
The x axis should be oriented along
Correct
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 .
=B*cos(theta),B*sin(theta)Solution Requested
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 ).
=A + B*cos(theta),B*sin(theta)Solution Requested
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.
=−1100,26.00 mSolution Requested
2.4Part A
Express
as an ordered triplet of values, separated by commas.
=0,0,10.0Allowed attempts exceeded; answer displayed
Part B
Find the magnitude of
.
=10.0Correct
Part C
Find the sine of the angle between
and
.
=0.707Allowed attempts exceeded; answer displayed
2. One Dimensional Kinematics
Part A
The variable is, in general, a function of time.
trueCorrect
Part B
The variable
falseCorrect
is, in general, a function of time.
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.
falseCorrect
Part D
The variable is, in general, a function of time.
falseCorrect
Part E
The variable is, in general, a function of time.
trueCorrect
The velocity always varies with time when the acceleration is nonzero.
Part F
The variable is, in general, a function of time.
trueCorrect
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.
sometimesCorrect
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.
alwaysCorrect
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.
falseCorrect
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?
Correct
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.
=0.5*a*t_1^2 + (0.5*a^2*t_1^2)/gSolution Requested
Part B
If the rocket's net acceleration is
rocket will reach?
for
, what is the maximum height the
Express your answer numerically in meters, using
.
=1470 mCorrect
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?
Correct
Part B
Which ball has the greater acceleration at the instant of release?
Neither; the accelerations of both balls are the same.Correct
Part C
Which ball has the greater speed at the instant of release?
Neither; the speeds are the same.Correct
Part D
Which ball has the greater average speed during the 1-s interval after release (assuming
neither hits the ground during that time)?
the ball thrown downward
Correct
Part E
Which ball hits the ground with greater speed?
Neither; the balls hit the ground with the same speed.Correct
3.4
Part A
At what time(s) do the rockets have the same velocity?
at some instant in time between
Correct
and
Part B
At what time(s) do the rockets have the same x position?
at times
Correct
and
Part C
At what time(s) do the two rockets have the same acceleration?
at no time shown in the figureCorrect
Part D
The motion of the rocket labeled A is an example of motion with uniform (i.e., constant)
__________.
and nonzero acceleration
Correct
Part E
The motion of the rocket labeled B is an example of motion with uniform (i.e., constant)
__________.
velocity
Correct
Part F
At what time(s) is rocket A ahead of rocket B?
before
Correct
and after
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
=v_0/a_0Solution Requested
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 .
=v_0/a_0Correct
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.
=(v_0^2)/a_0Solution Requested
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
=v_0/a_0Solution Requested
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 .
=v_0/a_0Correct
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.
=(v_0^2)/a_0Solution Requested
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