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What is the magnitude of What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ? A) 7.07 B) 2.00 C) 10.76 D) 6.78 E) 8.12 + What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ? A) 7.07 B) 2.00 C) 10.76 D) 6.78 E) 8.12 + What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ? A) 7.07 B) 2.00 C) 10.76 D) 6.78 E) 8.12 , where What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ? A) 7.07 B) 2.00 C) 10.76 D) 6.78 E) 8.12 = 1.00 What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ? A) 7.07 B) 2.00 C) 10.76 D) 6.78 E) 8.12 + 4.00 What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ? A) 7.07 B) 2.00 C) 10.76 D) 6.78 E) 8.12 - 1.00 What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ? A) 7.07 B) 2.00 C) 10.76 D) 6.78 E) 8.12 , What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ? A) 7.07 B) 2.00 C) 10.76 D) 6.78 E) 8.12 = 3.00 What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ? A) 7.07 B) 2.00 C) 10.76 D) 6.78 E) 8.12 - 1.00 What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ? A) 7.07 B) 2.00 C) 10.76 D) 6.78 E) 8.12 - 4.00 What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ? A) 7.07 B) 2.00 C) 10.76 D) 6.78 E) 8.12 and What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ? A) 7.07 B) 2.00 C) 10.76 D) 6.78 E) 8.12 = -1.00 What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ? A) 7.07 B) 2.00 C) 10.76 D) 6.78 E) 8.12 + 1.00 What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ? A) 7.07 B) 2.00 C) 10.76 D) 6.78 E) 8.12 ?


A) 7.07
B) 2.00
C) 10.76
D) 6.78
E) 8.12

F) D) and E)
G) None of the above

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As shown in the figure, three force vectors act on an object. The magnitudes of the forces as shown in the figure are As shown in the figure, three force vectors act on an object. The magnitudes of the forces as shown in the figure are = 80.0 N, = 60.0 N, and = 40.0 N, where N is the standard SI unit of force. The resultant force acting on the object is given by A) 180 N at an angle 60.0° with respect to +x-axis. B) 60.0 N at an angle 90.0° with respect to +x-axis. C) 20.0 N at an angle 34.3° with respect to +x-axis. D) 35.5 N at an angle 34.3° with respect to +x-axis. E) 40.0 N at an angle 60.0° with respect to +x-axis. = 80.0 N, As shown in the figure, three force vectors act on an object. The magnitudes of the forces as shown in the figure are = 80.0 N, = 60.0 N, and = 40.0 N, where N is the standard SI unit of force. The resultant force acting on the object is given by A) 180 N at an angle 60.0° with respect to +x-axis. B) 60.0 N at an angle 90.0° with respect to +x-axis. C) 20.0 N at an angle 34.3° with respect to +x-axis. D) 35.5 N at an angle 34.3° with respect to +x-axis. E) 40.0 N at an angle 60.0° with respect to +x-axis. = 60.0 N, and As shown in the figure, three force vectors act on an object. The magnitudes of the forces as shown in the figure are = 80.0 N, = 60.0 N, and = 40.0 N, where N is the standard SI unit of force. The resultant force acting on the object is given by A) 180 N at an angle 60.0° with respect to +x-axis. B) 60.0 N at an angle 90.0° with respect to +x-axis. C) 20.0 N at an angle 34.3° with respect to +x-axis. D) 35.5 N at an angle 34.3° with respect to +x-axis. E) 40.0 N at an angle 60.0° with respect to +x-axis. = 40.0 N, where N is the standard SI unit of force. The resultant force acting on the object is given by As shown in the figure, three force vectors act on an object. The magnitudes of the forces as shown in the figure are = 80.0 N, = 60.0 N, and = 40.0 N, where N is the standard SI unit of force. The resultant force acting on the object is given by A) 180 N at an angle 60.0° with respect to +x-axis. B) 60.0 N at an angle 90.0° with respect to +x-axis. C) 20.0 N at an angle 34.3° with respect to +x-axis. D) 35.5 N at an angle 34.3° with respect to +x-axis. E) 40.0 N at an angle 60.0° with respect to +x-axis.


A) 180 N at an angle 60.0° with respect to +x-axis.
B) 60.0 N at an angle 90.0° with respect to +x-axis.
C) 20.0 N at an angle 34.3° with respect to +x-axis.
D) 35.5 N at an angle 34.3° with respect to +x-axis.
E) 40.0 N at an angle 60.0° with respect to +x-axis.

F) C) and D)
G) B) and D)

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Vector Vector has a magnitude of 75.0 cm and points at 30° above the positive x-axis. Vector has a magnitude of 25.0 cm and points along the negative x-axis. Vector has a magnitude of 40.0 cm and points at 45° below the negative x-axis. (a) Determine the x and y components of Vector . (b) Determine the x and y components of Vector . (c) Determine the x and y components of Vector . (d) Determine x and y components of the sum of these three vectors. (e) Determine the magnitude and direction of the sum of these three vectors. has a magnitude of 75.0 cm and points at 30° above the positive x-axis. Vector Vector has a magnitude of 75.0 cm and points at 30° above the positive x-axis. Vector has a magnitude of 25.0 cm and points along the negative x-axis. Vector has a magnitude of 40.0 cm and points at 45° below the negative x-axis. (a) Determine the x and y components of Vector . (b) Determine the x and y components of Vector . (c) Determine the x and y components of Vector . (d) Determine x and y components of the sum of these three vectors. (e) Determine the magnitude and direction of the sum of these three vectors. has a magnitude of 25.0 cm and points along the negative x-axis. Vector Vector has a magnitude of 75.0 cm and points at 30° above the positive x-axis. Vector has a magnitude of 25.0 cm and points along the negative x-axis. Vector has a magnitude of 40.0 cm and points at 45° below the negative x-axis. (a) Determine the x and y components of Vector . (b) Determine the x and y components of Vector . (c) Determine the x and y components of Vector . (d) Determine x and y components of the sum of these three vectors. (e) Determine the magnitude and direction of the sum of these three vectors. has a magnitude of 40.0 cm and points at 45° below the negative x-axis. (a) Determine the x and y components of Vector Vector has a magnitude of 75.0 cm and points at 30° above the positive x-axis. Vector has a magnitude of 25.0 cm and points along the negative x-axis. Vector has a magnitude of 40.0 cm and points at 45° below the negative x-axis. (a) Determine the x and y components of Vector . (b) Determine the x and y components of Vector . (c) Determine the x and y components of Vector . (d) Determine x and y components of the sum of these three vectors. (e) Determine the magnitude and direction of the sum of these three vectors. . (b) Determine the x and y components of Vector Vector has a magnitude of 75.0 cm and points at 30° above the positive x-axis. Vector has a magnitude of 25.0 cm and points along the negative x-axis. Vector has a magnitude of 40.0 cm and points at 45° below the negative x-axis. (a) Determine the x and y components of Vector . (b) Determine the x and y components of Vector . (c) Determine the x and y components of Vector . (d) Determine x and y components of the sum of these three vectors. (e) Determine the magnitude and direction of the sum of these three vectors. . (c) Determine the x and y components of Vector Vector has a magnitude of 75.0 cm and points at 30° above the positive x-axis. Vector has a magnitude of 25.0 cm and points along the negative x-axis. Vector has a magnitude of 40.0 cm and points at 45° below the negative x-axis. (a) Determine the x and y components of Vector . (b) Determine the x and y components of Vector . (c) Determine the x and y components of Vector . (d) Determine x and y components of the sum of these three vectors. (e) Determine the magnitude and direction of the sum of these three vectors. . (d) Determine x and y components of the sum of these three vectors. (e) Determine the magnitude and direction of the sum of these three vectors.

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(a) blured image = 65 cm, blured image = 38 cm
(b) blured image = ...

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Vectors Vectors and are shown in the figure. Vector is given by = - . The magnitude of vector is 16.0 units, and the magnitude of vector is 7.00 units. What is the angle of vector , measured counterclockwise from the +x-axis? A) 16.9° B) 22.4° C) 73.1° D) 287° E) 292° and Vectors and are shown in the figure. Vector is given by = - . The magnitude of vector is 16.0 units, and the magnitude of vector is 7.00 units. What is the angle of vector , measured counterclockwise from the +x-axis? A) 16.9° B) 22.4° C) 73.1° D) 287° E) 292° are shown in the figure. Vector Vectors and are shown in the figure. Vector is given by = - . The magnitude of vector is 16.0 units, and the magnitude of vector is 7.00 units. What is the angle of vector , measured counterclockwise from the +x-axis? A) 16.9° B) 22.4° C) 73.1° D) 287° E) 292° is given by Vectors and are shown in the figure. Vector is given by = - . The magnitude of vector is 16.0 units, and the magnitude of vector is 7.00 units. What is the angle of vector , measured counterclockwise from the +x-axis? A) 16.9° B) 22.4° C) 73.1° D) 287° E) 292° = Vectors and are shown in the figure. Vector is given by = - . The magnitude of vector is 16.0 units, and the magnitude of vector is 7.00 units. What is the angle of vector , measured counterclockwise from the +x-axis? A) 16.9° B) 22.4° C) 73.1° D) 287° E) 292° - Vectors and are shown in the figure. Vector is given by = - . The magnitude of vector is 16.0 units, and the magnitude of vector is 7.00 units. What is the angle of vector , measured counterclockwise from the +x-axis? A) 16.9° B) 22.4° C) 73.1° D) 287° E) 292° . The magnitude of vector Vectors and are shown in the figure. Vector is given by = - . The magnitude of vector is 16.0 units, and the magnitude of vector is 7.00 units. What is the angle of vector , measured counterclockwise from the +x-axis? A) 16.9° B) 22.4° C) 73.1° D) 287° E) 292° is 16.0 units, and the magnitude of vector Vectors and are shown in the figure. Vector is given by = - . The magnitude of vector is 16.0 units, and the magnitude of vector is 7.00 units. What is the angle of vector , measured counterclockwise from the +x-axis? A) 16.9° B) 22.4° C) 73.1° D) 287° E) 292° is 7.00 units. What is the angle of vector Vectors and are shown in the figure. Vector is given by = - . The magnitude of vector is 16.0 units, and the magnitude of vector is 7.00 units. What is the angle of vector , measured counterclockwise from the +x-axis? A) 16.9° B) 22.4° C) 73.1° D) 287° E) 292° , measured counterclockwise from the +x-axis? Vectors and are shown in the figure. Vector is given by = - . The magnitude of vector is 16.0 units, and the magnitude of vector is 7.00 units. What is the angle of vector , measured counterclockwise from the +x-axis? A) 16.9° B) 22.4° C) 73.1° D) 287° E) 292°


A) 16.9°
B) 22.4°
C) 73.1°
D) 287°
E) 292°

F) A) and B)
G) A) and E)

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A helicopter is flying horizontally with a speed of 444 m/s over a hill that slopes upward with a 2% grade (that is, the "rise" is 2% of the "run") . What is the component of the helicopter's velocity perpendicular to the sloping surface of the hill?


A) 8.9 m/s
B) 220 m/s
C) 435 m/s
D) 444 m/s

E) A) and B)
F) A) and C)

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If all the components of a vector are equal to 1, then that vector is a unit vector.


A) True
B) False

C) A) and B)
D) undefined

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An apple falls from an apple tree growing on a 20° slope. The apple hits the ground with an impact velocity of 16.2 m/s straight downward. What is the component of the apple's impact velocity parallel to the surface of the slope?


A) 5.5 m/s
B) 8.7 m/s
C) 12 m/s
D) 15 m/s

E) All of the above
F) A) and B)

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Vector Vector has a magnitude of 5.5 cm and points along the x-axis. Vector has a magnitude of 7.5 cm and points at +30° above the negative x-axis. (a) Determine the x and y components of Vector . (b) Determine the x and y components of Vector (c) Determine x and y components of the sum of these two vectors. (d) Determine the magnitude and direction of the sum of these two vectors. has a magnitude of 5.5 cm and points along the x-axis. Vector Vector has a magnitude of 5.5 cm and points along the x-axis. Vector has a magnitude of 7.5 cm and points at +30° above the negative x-axis. (a) Determine the x and y components of Vector . (b) Determine the x and y components of Vector (c) Determine x and y components of the sum of these two vectors. (d) Determine the magnitude and direction of the sum of these two vectors. has a magnitude of 7.5 cm and points at +30° above the negative x-axis. (a) Determine the x and y components of Vector Vector has a magnitude of 5.5 cm and points along the x-axis. Vector has a magnitude of 7.5 cm and points at +30° above the negative x-axis. (a) Determine the x and y components of Vector . (b) Determine the x and y components of Vector (c) Determine x and y components of the sum of these two vectors. (d) Determine the magnitude and direction of the sum of these two vectors. . (b) Determine the x and y components of Vector Vector has a magnitude of 5.5 cm and points along the x-axis. Vector has a magnitude of 7.5 cm and points at +30° above the negative x-axis. (a) Determine the x and y components of Vector . (b) Determine the x and y components of Vector (c) Determine x and y components of the sum of these two vectors. (d) Determine the magnitude and direction of the sum of these two vectors. (c) Determine x and y components of the sum of these two vectors. (d) Determine the magnitude and direction of the sum of these two vectors.

Correct Answer

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(a) blured image = 5.5 cm, blured image = 0
(b) blured image = -6....

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Vector Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00 = -3.00 Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00 + 3.00 Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00 and vector Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00 = 3.00 Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00 + 4.00 Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00 . What is vector Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00 = Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00 + Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00 ?


A) 0.00 Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00 + 3.00 Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00
B) 7.00 Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00 + 7.00 Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00
C) -3.00 Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00 + 7.00 Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00
D) 0.00 Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00 + 7.00 Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00
E) -3.00 Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00 -3.00 Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ? A) 0.00 + 3.00 B) 7.00 + 7.00 C) -3.00 + 7.00 D) 0.00 + 7.00 E) -3.00 -3.00

F) B) and C)
G) C) and D)

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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 vector components, determine how far the airplane ends up from its starting point.


A) 79 km
B) 81 km
C) 82 km
D) 78 km
E) 76 km

F) A) and E)
G) A) and B)

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You walk 53 m to the north, then turn 60° to your right and walk another You walk 53 m to the north, then turn 60° to your right and walk another Determine the direction of your displacement vector. Express your answer as an angle relative to east. A) 63° N of E B) 50° N of E C) 57° N of E D) 69° N of E Determine the direction of your displacement vector. Express your answer as an angle relative to east.


A) 63° N of E
B) 50° N of E
C) 57° N of E
D) 69° N of E

E) C) and D)
F) None of the above

Correct Answer

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If the magnitude of vector If the magnitude of vector is less than the magnitude of vector , then the x component of is less than the x component of . A) True B) False is less than the magnitude of vector If the magnitude of vector is less than the magnitude of vector , then the x component of is less than the x component of . A) True B) False , then the x component of If the magnitude of vector is less than the magnitude of vector , then the x component of is less than the x component of . A) True B) False is less than the x component of If the magnitude of vector is less than the magnitude of vector , then the x component of is less than the x component of . A) True B) False .


A) True
B) False

C) A) and B)
D) undefined

Correct Answer

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Vector Vector has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis. What are the x and y components of vector . A) A<sub>x</sub> = 3.83 and A<sub>y</sub> = 3.21 B) A<sub>x</sub> = 3.83 and A<sub>y</sub> = -3.21 C) A<sub>x</sub> = -3.21 and A<sub>y</sub> = -3.83 D) A<sub>x</sub> = -3.21 and A<sub>y</sub> = 3.83 E) A<sub>x</sub> = 4.29 and A<sub>y</sub> = 2.16 has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis. What are the x and y components of vector Vector has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis. What are the x and y components of vector . A) A<sub>x</sub> = 3.83 and A<sub>y</sub> = 3.21 B) A<sub>x</sub> = 3.83 and A<sub>y</sub> = -3.21 C) A<sub>x</sub> = -3.21 and A<sub>y</sub> = -3.83 D) A<sub>x</sub> = -3.21 and A<sub>y</sub> = 3.83 E) A<sub>x</sub> = 4.29 and A<sub>y</sub> = 2.16 .


A) Ax = 3.83 and Ay = 3.21
B) Ax = 3.83 and Ay = -3.21
C) Ax = -3.21 and Ay = -3.83
D) Ax = -3.21 and Ay = 3.83
E) Ax = 4.29 and Ay = 2.16

F) A) and D)
G) A) and E)

Correct Answer

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