QUESTION
12. 3. 31. 오전 1:16MasteringPhysics: Assignment Print View
Week 3 Chapter 3 2D Motion
Due: 11:59pm on Friday, March 30, 2012
Note: To understand how points are awarded, read your instructor’s Grading Policy.
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Item 1
In general it is best to conceptualize vectors as arrows in space, and then to make calculations with
them using their components. (You must first specify a coordinate system in order to find the
components of each arrow.) This problem gives you some practice with the components.
Let vectors , , and . Calculate the following, and express
your answers as ordered triplets of values separated by commas.
Part A
ANSWER:
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Part B
ANSWER:
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Part C
ANSWER:
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Part D
ANSWER:
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Part E
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ANSWER:
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[ Print ]
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12. 3. 31. 오전 1:16MasteringPhysics: Assignment Print View
Part F
ANSWER:
=
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Item 2
Learning Goal: To understand the basic concepts of projectile motion.
Projectile motion may seem rather complex at first. However, by breaking it down into components, you will
find that it is really no different than the one-dimensional motions that you have already studied.
One of the most often used techniques in physics is to divide two- and three-dimensional quantities into
components. For instance, in projectile motion, a particle has some initial velocity . In general, this
velocity can point in any direction on the xy plane and can have any magnitude. To make a problem more
managable, it is common to break up such a quantity into its x component and its y component .
Consider a particle with initial velocity that has magnitude 12.0 and is directed 60.0
above the negative x axis.
Part A
What is the x component of ?
Express your answer in meters per second.
ANSWER:
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Part B
What is the y component of ?
Express your answer in meters per second.
ANSWER:
=
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Breaking up the velocities into components is particularly useful when the components do not
affect each other. Eventually, you will learn about situations in which the components of velocity
do affect one another, but for now you will only be looking at problems where they do not. So, if
there is acceleration in the x direction but not in the y direction, then the x component of the
velocity will change, but the y component of the velocity will not.
Part C
Look at this applet. The motion diagram for a projectile is displayed, as are the motion diagrams
for each component. The x-component motion diagram is what you would get if you shined a
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Both the vertical and horizontal components exhibit
The vertical component exhibits constant-velocity motion,
The vertical component exhibits motion with constant
Both the vertical and horizontal components exhibit
12. 3. 31. 오전 1:16MasteringPhysics: Assignment Print View
spotlight down on the particle as it moved and recorded the motion of its shadow. Similarly, if you
shined a spotlight to the left and recorded the particle’s shadow, you would get the motion
diagram for its y component. How would you describe the two motion diagrams for the
components?
ANSWER:
motion with constant nonzero acceleration.
nonzero acceleration, whereas the horizontal component
exhibits constant-velocity motion.
whereas the horizontal component exhibits motion with
constant nonzero acceleration.
motion with constant velocity.
Transition will be visible after you complete previous part(s).
Part D
Part E
A swimmer wants to cross a river, from
point A to point B, as shown in the figure.
The distance (from A to C) is 200 , the
distance (from C to B) is 150 , and the
speed of the current in the river is 5
. Suppose that the swimmer’s
velocity relative to the water makes an
angle of with the line from
A to C, as indicated in the figure.
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Item 3
Part A
To swim directly from A to B, what speed , relative to the water, should the swimmer have?
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Answer
not
displayed
12. 3. 31. 오전 1:16MasteringPhysics: Assignment Print View
Hint A.1 Use the motion in the y direction
Hint A.2 Use the motion in the x direction
Hint A.3 Solve for
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Express the swimmer’s speed numerically, to three significant figures, in kilometers per
hour.
ANSWER:
=
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Item 4
A quarterback is set up to throw the football to a receiver who is running with a constant velocity
directly away from the quarterback and is now a distance away from the quarterback. The
quarterback figures that the ball must be thrown at an angle to the horizontal and he estimates
that the receiver must catch the ball a time interval after it is thrown to avoid having opposition
players prevent the receiver from making the catch. In the following you may assume that the ball is
thrown and caught at the same height above the level playing field. Assume that the y coordinate of
the ball at the instant it is thrown or caught is and that the horizontal position of the
quaterback is .
Use for the magnitude of the acceleration
due to gravity, and use the pictured inertial
coordinate system when solving the problem.
Part A
Find , the vertical component of the velocity of the ball when the quarterback releases it.
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Hint A.1 Equation of motion in y direction
Hint A.2 Height at which the ball is caught,
Express in terms of and .
ANSWER:
=
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Part B
Find , the initial horizontal component of velocity of the ball.
Hint B.1 Receiver’s position
Hint B.2 Football’s position
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Express your answer for in terms of , , and .
ANSWER:
=
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Part C
Find the speed with which the quarterback must throw the ball.
Hint C.1 How to approach the problem
Answer in terms of , , , and .
ANSWER:
=
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Answer not displayed
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Part D
Assuming that the quarterback throws the ball with speed , find the angle above the
horizontal at which he should throw it.
Hint D.1 Find angle from and
Hint not displayed
Your solution should contain an inverse trig function (entered as asin, acos, or atan). Give
your answer in terms of already known quantities, , , and .
ANSWER:
=
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Item 5
A sailboard is sailing at 6.5 when a gust of wind hits, causing it to accelerate at 0.48 at a
35 angle to its original direction of motion.
Part A
If the acceleration lasts 6.3 , what is the board’s net displacement during the wind gust?
Express your answer using two significant figures.
ANSWER:
=
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Item 6
Ink droplets in an ink-jet printer are ejected horizontally at 12 and travel a horizontal distance
of 1.0 to the paper.
Part A
How far do they fall in this interval?
Express your answer using two significant figures.
ANSWER:
=
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Item 7
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Part A
If you can hit a golf ball 180 on Earth, how far can you hit it on the Moon? (Your answer is an
underestimate because the distance on Earth is restricted by air resistance as well as by a larger
.)
ANSWER:
=
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Item 8
An alpine rescue team is using a slingshot to send an emergency medical packet to climbers
stranded on a ledge, as shown in the figure below.
Part A
What should be the launch speed from the slingshot?
Express your answer using two significant figures.
ANSWER:
=
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Item 9
An object’s position as a function of time is given by , where is
time in seconds.
Part A
What is the object’s position at ?
Express your answer as a comma-separated pair of components. Express your answer
using two significant figures.
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12. 3. 31. 오전 1:16MasteringPhysics: Assignment Print View
ANSWER:
=
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Part B
What is its average velocity in the interval from to ?
Express your answer as a comma-separated pair of components. Express your answer
using two significant figures.
ANSWER:
=
Answer not displayed
Part C
What is its instantaneous velocity at ?
Express your answer as a comma-separated pair of components. Express your answer
using two significant figures.
ANSWER:
=
Score Summary:
Answer not displayed
Your score on this assignment is 0%.
You received 0 out of a possible total of 9 points.
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SOLUTION
1. Given,
(A)
(B)
(C)
(D)
(E)
(F)
- The magnitude of initial velocity
Angle made with the negative x-axis
(A) The x-component of velocity
(B) They-component of velocity
3. (A)
Motion along the vertical direction is
Motion along horizontal direction is
Therefore, we get
5. Given,
Initial velocity
The horizontal displacement
The vertical displacement
Therefore, the net displacement is
6. Given,
Therefore, the time taken is
Therefore, the object will fall by the distance
7. (A) Given, distance hit on earth=180m
We know that on moon, the acceleration due to gravity is
Therefore, the distance hit on moon will be 6 times that of the earth.
Therefore, the golf ball will be hit by the distance on the moon
8. Given,
We know that,
9. Given,
Where, t is time in seconds.
(A) Object’s position at t=2.0s
(B) Average velocity in the interval from t=0 to t=2.0s
(C) The instantaneous velocity at t=2.0s
JE28
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