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Test 1Due: 11:59pm on Sunday, September 12, 2010
Note: You will receive no credit for late submissions. To learn more, read your instructor's Grading Policy
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Exercise 1.12
A useful and easy-to-remember approximate value for the number of seconds in a year is .
Part A
Determine the percent error in this approximate value. (There are 365.24 days in one year.)
ANSWER: 0.446 Correct
Exercise 1.28
Part A
How many dollar bills would you have to stack to reach the moon? (Depending on age, dollar bills can be stacked with about 2-3 per millimeter.)
Express your answer using one significant figure.
ANSWER: 1.0×1012 All attempts used; correct answer displayed dollar bills
Exercise 1.45
Part A
Use vector components to find the magnitude of the vector needed to balance the two vectors shown in the figure . Let the 625- vector be along the -y-axis and let the +x-axis be perpendicular to it toward the right.
ANSWER: 781 Correct
Part B
Find the direction of the vector needed to balance this two vectors.
ANSWER: 166 Correct counterclockwise from -axis
Exercise 1.47
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Write each vector in the figure in terms of the unit vectors and .
Part A
ANSWER: =
Correct
Part B
ANSWER: =
Correct
Part C
ANSWER: =
Correct
Part D
ANSWER: =
Correct
Problem 1.76On a training flight, a student pilot flies from Lincoln, Nebraska to Clarinda, Iowa, then to St. Joseph, Missouri, and then to Manhattan, Kansas . The directions are shown relative to north: is north, is east, is south, and is west.
Part A
Use the method of components to find the distance she has to fly from Manhattan to get back to Lincoln.
ANSWER: 189 Correct
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Part B
Find the direction (relative to north) she must fly to get there.
ANSWER: = -10.5
Correct
Problem 1.82You are hungry and decide to go to your favorite neighborhood fast-food restaurant. You leave your apartment and take the elevator 10 flights down (each flight is 3.0 ) and then go 15 south to the apartment exit. You then proceed 0.2 east, turn north, and go 0.1 to the entrance of the restaurant.
Part A
Determine the displacement from your apartment to the restaurant. Use unit vector notation for your answer, being sure to make clear your choice of coordinates.
Take the beginning of the journey as the origin, with north being the y-direction, east the x-direction, and the z-axis vertical.
ANSWER:
Correct
Part B
How far did you travel along the path you took from your apartment to the restaurant?
ANSWER: 345 Correct
Part C
What is the magnitude of the displacement you calculated in part A?
ANSWER: = 219
Correct
Problem 1.92
When two vectors and are drawn from a common point, the angle between them is .
Part A
If and have the same magnitude, for which value of will their vector sum have the same magnitude as or ?
ANSWER: = 120
Correct
Problem 1.94
Part A
Given two vectors and . Obtain a unit vector perpendicular to these two vectors.
Express your answer as a unit vector in the form , , where the x, y, and z components are separated by commas.
ANSWER: = -0.720,0.332,-0.609
Correct
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Test Your Understanding 1.9: Unit Vectors
Part A
Rank the following vectors from largest to smallest magnitude.
ANSWER:
View
Correct
The magnitude of a vector is . Note that the value of the magnitude does not depend on
whether the components , , and are positive or negative.
Problem 1.91
The two vectors and are drawn from a common point, and .
Part A
Show that if , the angle between the vectors and is 90 .
ANSWER: My Answer:
Part B
Show that if , the angle between the vectors and is greater than 90 .
ANSWER: My Answer:
Part C
Show that if , the angle between the vectors and is between 0 and 90 .
ANSWER: My Answer:
Exercise 1.15
Part A
Estimate the percent error in measuring a distance of about 85 with a meter stick.
Express your answer using two significant figures.
ANSWER: 0.12 Correct
Part B
Estimate the percent error in measuring a mass of about 16 with a chemical balance.
Express your answer using two significant figures.
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ANSWER: 6.3×10−3 Correct
Part C
Estimate the percent error in measuring a time interval of about 8 with a stopwatch.
Express your answer using two significant figures.
ANSWER: 2.1×10−2 Correct
Exercise 1.16
A rectangular piece of aluminum is 5.20 long and 1.80 wide.
Part A
Find the area of the rectangle.
ANSWER: 9.36 Correct
Part B
Find the uncertainty in the area.
Express your answer using one significant figure.
ANSWER: 7×10−2 Correct
Exercise 1.17
As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of and a thickness of 4.5×10−2 0.005 .
Part A
Find the average volume of a cookie.
Express your answer using two significant figures.
ANSWER: 2.6 Correct
Part B
Find the uncertainty in the volume of a cookie.
Express your answer using one significant figure.
ANSWER: 0.3 Correct
Part C
Find the ratio of the diameter to the thickness.
Express your answer using two significant figures.
ANSWER: 190 Correct
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Part D
Find the uncertainty in this ratio.
Express your answer using one significant figure.
ANSWER: 20 Correct
Exercise 1.37
A rocket fires two engines simultaneously. One produces a thrust of 690 directly forward while the other gives a thrust of 480 at an angle 16.2 above the forward direction.
Part A
Find the magnitude of the resultant force which these engines exert on the rocket.
ANSWER: 1160 Correct N
Part B
Find the deviation of the direction (relative to the forward direction) of the resultant force which these engines exert on the rocket.
ANSWER: 6.64 Correct
Exercise 1.46
Two ropes in a vertical plane exert equal magnitude forces on a hanging weight but pull with an angle of 86.0 between them.
Part A
What pull does each one exert if their resultant pull is 402 directly upward?
ANSWER: 275 Correct
Problem 1.65
Iron has a property such that a 1.00 volume has a mass of (density equals ). You want to manufacture iron
into cubes and spheres.
Part A
Find the length of the side of a cube of iron that has a mass of 140 .
ANSWER: 2.61 Correct
Part B
Find the radius of a solid sphere of iron that has a mass of 140 .
ANSWER: 1.62 Correct
Problem 1.73
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A spelunker is surveying a cave. She follows a passage that takes her a distance 178 straight west, then a distance 213 in a direction 45.0 east of south, then a distance 274 at 30.0 east of north. After a fourth unmeasured displacement she finds herself back where she started.
Part A
Use the method of components to determine the magnitude of the fourth displacement.
ANSWER: 140 Correct m
Part B
Use the method of components to determine the direction of the fourth displacement.
ANSWER: 38.3 Correct South of West
Problem 1.78: Getting Back
An explorer in the dense jungles of equatorial Africa leaves his hut. He takes 43 steps at an angle 45 north of east, then 80 steps at an angle 60 north of west, then 49 steps due south. Assume his steps all have equal length. Save him from becoming hopelessly lost in the jungle by giving him the displacement, calculated using the method of components, that will return him to his hut.
Part A
What is the magnitude of the displacement that will return the explorer to his hut?
Express your answer using two significant figures.
ANSWER: 52 Correct steps
Part B
What is the direction of the displacement that will return the explorer to his hut?
Express your answer using two significant figures.
ANSWER: = 11
Correct East of South
Problem 1.79
A ship leaves the island of Guam and sails a distance 275 at an angle 47.0 north of west.
Part A
In which direction must it now head so that its resultant displacement will be 130 directly east of Guam? (Express your answer as an angle measured south of east)
ANSWER: = 32.3
Correct south of east
Part B
How far must it sail so that its resultant displacement will be 130 directly east of Guam?
ANSWER: 376 Correct
Problem 1.84
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You are camping with two friends, Joe and Karl. Since all three of you like your privacy, you don't pitch your tents close together. Joe's tent is 25.0 from yours, in the direction 24.0 north of east. Karl's tent is 43.5 from yours, in the direction 36.5 south of east.
Part A
What is the distance between Karl's tent and Joe's tent?
ANSWER: = 38.0
Correct
Multiple Choice Question - 1.19
Part A
A vector is given as follows:
The angle between vector and the y-axis, in degrees, is closest to:
ANSWER: 61
151
90
119
29
Correct
Multiple Choice Question - 1.26
Part A
An airplane undergoes the following displacements: First, it flies 66 km in a direction 30 east of north. Next, it flies 49 km due south. Finally, it flies 100 km 30 north of west. Using analytical methods, determine how far the airplane ends up from its starting point.
ANSWER: 80.7 km
79.1 km
82.3 km
75.9 km
77.5 km
Correct
Short Answer Question - 1.3
Part A
Find the vector product × of the two vectors and , where = 7 + 8 and = -6 - 3 . Express your result in terms of the
, , and unit vectors.
ANSWER:
Correct
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Short Answer Question - 1.5
Part A
In the figure, the magnitude of vector is 18.0 units, and the magnitude of vector is 12.0 units. What vector must be added to the
vectors and in the figure so that the resultant of these three vectors points in the - -direction and has a magnitude of 7.50 units? Use
vector components to find your answer, and express vector by giving its magnitude and the angle in degrees it makes with the x-axis taking
counterclockwise to be positive.
Enter your answers numerically separated by a comma.
ANSWER: 15.5,209 All attempts used; correct answer displayed
Score Summary:Your score on this assignment is 84.1%. You received 84.11 out of a possible total of 100 points.
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