Question 1

In a 2-dimensional Cartesian system,the x-component of a vector is known,and the angle between vector and x-axis is known.Which operation is used to calculate the magnitude of the vector? (taken with respect to the x-component)

Accepted Answer

To calculate the magnitude of the vector, we use the formula:
Magnitude = x-component / cosine(angle between vector and x-axis)
Therefore, we need to divide the x-component by cosine(angle between vector and x-axis) to get the magnitude.

Question 2

A car is initially moving at 20 m/s east,and a little while later it is moving at 10 m/s north.Which of the following best describes the orientation of the average acceleration during this time interval?

Accepted Answer

The car is experiencing a change in velocity that is both to the north and to the west. Thus, the average acceleration vector is in the direction that is north of west.

Question 3

An object moves at a constant velocity of 16 m/s to the southwest for an interval of 30 s.Halfway through this interval,what is the magnitude of its instantaneous velocity?
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Accepted Answer

The magnitude of instantaneous velocity is the magnitude of the constant velocity, which is 16 m/s at any given time during the interval. Therefore, the magnitude of the instantaneous velocity halfway through the interval is also 16 m/s.

Question 4

Which of the following is an example of a vector quantity?

Accepted Answer

Vector quantities have both magnitude and direction, and velocity is a vector quantity as it has both speed and direction. Temperature, volume, and mass are scalar quantities as they only have magnitude.

Question 5

The following force vectors act on an object: i)55.0 newtons at 45.0° north of east and ii)25.0 newtons at 30.0° south of east.Which of the following represents the magnitude of the resultant and its angle relative to the easterly direction?
​

Accepted Answer

The resultant vector is calculated by breaking each force into its components, summing them, and then finding the magnitude and direction. The resultant magnitude is approximately 66 newtons, and the angle relative to the easterly direction is about 23.6°.

Question 6

When three vectors are added graphically and form a closed triangle,the largest enclosed angle between any two of the vectors cannot be greater than

Accepted Answer

When three vectors form a closed triangle graphically, it means the sum of these vectors is zero. The largest angle in any triangle cannot exceed 180°, as this is the straight angle, beyond which the vectors would not form a closed triangle but would start to 'open up'. Therefore, the largest enclosed angle between any two vectors in such a scenario cannot be greater than 180°.

Question 7

An object,initially moving in the negative x-direction,is subjected to a change in velocity in the positive y-direction.If the resulting velocity vector is drawn from the origin,into which quadrant does this vector point?

Accepted Answer

Since the object initially moved in the negative x-direction, its velocity vector was in the negative x-axis direction (i.e. quadrant III or IV). The change in velocity in the positive y-direction means that the resulting velocity vector will have components in both the x and y directions. Therefore, the resulting vector will point in quadrant II or IV. However, since the question states that the vector is drawn from the origin, the resulting vector can only point in quadrant II. Therefore, the answer is B, which represents quadrant II.

Question 8

A student adds two vectors with magnitudes of 230 and 40.Which one of the following is the only possible choice for the magnitude of the resultant?

Accepted Answer

The answer of A student adds two vectors with magnitudes...

Question 9

A runner circles a track of radius 100 m one time in 100 s at a constant rate.The greatest change in his velocity from his starting velocity:

Accepted Answer

Since the runner is moving at a constant rate, his velocity is always tangential to the circle. Therefore, the only way his velocity can change is if his direction changes. The greatest change in direction occurs at the point farthest from the starting point, which is halfway around the track. Thus, the greatest change in velocity occurs at this point as well. Therefore, the correct answer is B.

Question 10

In a 2-dimensional Cartesian coordinate system the y-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function,with respect to the angle between vector and y-axis?

Accepted Answer

The y-component of a vector is equal to the vector's magnitude multiplied by the cosine of the angle between the vector and the y-axis.

Question 11

Find the resultant of the following two vectors: i)40 units due east and ii)100 units 30° north of west.
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Accepted Answer

We can find the resultant of the two vectors using the method of vector addition.

First, we draw a diagram to represent the two vectors.

40 units due east can be represented by a vector pointing to the right (or along the positive x-axis).

100 units 30° north of west can be represented by a vector pointing in the direction between north and west, but closer to west. We can draw this vector by first drawing a vector pointing due west (or along the negative x-axis), and then rotating it 30° clockwise.

We can now add the two vectors by placing them head-to-tail, i.e., by putting the tail of the second vector at the head of the first vector.

The resulting vector is the vector that starts at the tail of the first vector and ends at the head of the second vector. We can measure the magnitude and direction of this vector using a ruler and a protractor.

The magnitude of the resultant vector is approximately 68 units, and its direction is approximately 47° north of west. Therefore, the correct answer is D) 68 units 47° north of west.

Question 12

In a 2-dimensional Cartesian coordinate system the x-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function,with respect to the angle between vector and x-axis?

Accepted Answer

The x-component of a vector is found by multiplying the vector's magnitude by the cosine of the angle between the vector and the x-axis.

Question 13

When we subtract a velocity vector from another velocity vector,the result is

Accepted Answer

Subtracting one velocity vector from another gives a new velocity vector, representing the difference in velocities. This operation does not change the nature of the quantities involved; they remain vectors in the context of velocity.

Question 14

A taxicab moves five blocks due north,six blocks due east,and another three blocks due north.Assume all blocks are of equal size.What is the magnitude of the taxi's displacement,start to finish?
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Accepted Answer

The taxi's total displacement is the straight-line distance from the starting point to the ending point. It moves a total of 8 blocks north (5 + 3) and 6 blocks east. Using the Pythagorean theorem, the displacement is √(8² + 6²) = √(64 + 36) = √100 = 10 blocks.

Question 15

The first displacement is 8 m,and the second displacement is 4 m.They cannot add together to give a total displacement of:
​

Accepted Answer

Displacements are vector quantities and they have both magnitude and direction. The total displacement is the vector sum of individual displacements. If the two given displacements are in opposite directions, then their vector sum would be the difference of their magnitudes (8 m - 4 m = 4 m) in the direction of the larger displacement. However, if they are in the same direction, then their vector sum would be the sum of their magnitudes (8 m + 4 m = 12 m) in the same direction. In this case, since none of the answer choices matches the result of summing or subtracting the given displacements, we can conclude that they are not in the same or opposite directions, but rather they are perpendicular to each other. Therefore, using the Pythagorean theorem, we can find the magnitude of the total displacement as:
total displacement = sqrt((8 m)^2 + (4 m)^2) = sqrt(80) m approx. 8.9 m
This value is not included in the answer choices. Therefore, the correct answer is A) 3 m which is just a distractor that results from adding or subtracting the given displacements in the wrong way.

Question 16

Vector Is 2 m long,and vector Is 4 m long.The length of the sum of the vectors must be
​

Accepted Answer

The answer of Vector Is 2 m long,and vector Is...

Question 17

When we add a displacement vector to another displacement vector,the result is

Accepted Answer

When we add a displacement vector to another displacement vector, the result is another displacement vector. This is because displacement is a vector quantity that has both magnitude and direction, and vector addition involves adding the magnitudes and directions of the vectors to find the resultant vector. A velocity is also a vector quantity, but it involves a change in displacement over time. An acceleration is a vector quantity that involves a change in velocity over time. A scalar is a quantity that has only magnitude, such as speed or temperature.

Question 18

A hiker walks 200 m west and then walks 100 m north.In what direction is her resulting displacement?

Accepted Answer

The answer of A hiker walks 200 m west and...

Question 19

Vector Points north,and vector Points east.I=−,then  Points

Accepted Answer

The answer of Vector Points north,and vector Points east.I=−,then ...

Question 20

Which type of quantity is characterized by both magnitude and direction?

Accepted Answer

A vector is a type of quantity that is described by both magnitude (its size) and direction (the way it is pointing). Scalars, on the other hand, have only magnitude and no direction. Trigonometric and algebraic variables can be either scalar or vector quantities, depending on how they are defined and used in a particular context.

Quiz 3: Vectors and Two-Dimensional Motion

In a 2-dimensional Cartesian system,the x-component of a vector is known,and the angle between vector and x-axis is known.Which operation is used to calculate the magnitude of the vector? (taken with respect to the x-component)

A car is initially moving at 20 m/s east,and a little while later it is moving at 10 m/s north.Which of the following best describes the orientation of the average acceleration during this time interval?

An object moves at a constant velocity of 16 m/s to the southwest for an interval of 30 s.Halfway through this interval,what is the magnitude of its instantaneous velocity?

Which of the following is an example of a vector quantity?

The following force vectors act on an object: i) 55.0 newtons at 45.0° north of east and ii) 25.0 newtons at 30.0° south of east.Which of the following represents the magnitude of the resultant and its angle relative to the easterly direction?

When three vectors are added graphically and form a closed triangle,the largest enclosed angle between any two of the vectors cannot be greater than

An object,initially moving in the negative x-direction,is subjected to a change in velocity in the positive y-direction.If the resulting velocity vector is drawn from the origin,into which quadrant does this vector point?

A student adds two vectors with magnitudes of 230 and 40.Which one of the following is the only possible choice for the magnitude of the resultant?

A runner circles a track of radius 100 m one time in 100 s at a constant rate.The greatest change in his velocity from his starting velocity:

In a 2-dimensional Cartesian coordinate system the y-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function,with respect to the angle between vector and y-axis?

Find the resultant of the following two vectors: i) 40 units due east and ii) 100 units 30° north of west.

In a 2-dimensional Cartesian coordinate system the x-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function,with respect to the angle between vector and x-axis?

When we subtract a velocity vector from another velocity vector,the result is

A taxicab moves five blocks due north,six blocks due east,and another three blocks due north.Assume all blocks are of equal size.What is the magnitude of the taxi's displacement,start to finish?

The first displacement is 8 m,and the second displacement is 4 m.They cannot add together to give a total displacement of:

Vector Is 2 m long,and vector Is 4 m long.The length of the sum of the vectors must be

When we add a displacement vector to another displacement vector,the result is

A hiker walks 200 m west and then walks 100 m north.In what direction is her resulting displacement?

Vector Points north,and vector Points east.If=−,then vector11ec8726_cf4b_540b_8f60_37bcf0a2cf5d_TB34225555_11 Points

Which type of quantity is characterized by both magnitude and direction?

Quiz 3: Vectors and Two-Dimensional Motion

In a 2-dimensional Cartesian system,the x-component of a vector is known,and the angle between vector and x-axis is known.Which operation is used to calculate the magnitude of the vector? (taken with respect to the x-component)

A car is initially moving at 20 m/s east,and a little while later it is moving at 10 m/s north.Which of the following best describes the orientation of the average acceleration during this time interval?

An object moves at a constant velocity of 16 m/s to the southwest for an interval of 30 s.Halfway through this interval,what is the magnitude of its instantaneous velocity? ​

Which of the following is an example of a vector quantity?

The following force vectors act on an object: i) 55.0 newtons at 45.0° north of east and ii) 25.0 newtons at 30.0° south of east.Which of the following represents the magnitude of the resultant and its angle relative to the easterly direction? ​

When three vectors are added graphically and form a closed triangle,the largest enclosed angle between any two of the vectors cannot be greater than

An object,initially moving in the negative x-direction,is subjected to a change in velocity in the positive y-direction.If the resulting velocity vector is drawn from the origin,into which quadrant does this vector point?

A student adds two vectors with magnitudes of 230 and 40.Which one of the following is the only possible choice for the magnitude of the resultant?

A runner circles a track of radius 100 m one time in 100 s at a constant rate.The greatest change in his velocity from his starting velocity:

In a 2-dimensional Cartesian coordinate system the y-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function,with respect to the angle between vector and y-axis?

Find the resultant of the following two vectors: i) 40 units due east and ii) 100 units 30° north of west. ​

In a 2-dimensional Cartesian coordinate system the x-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function,with respect to the angle between vector and x-axis?

When we subtract a velocity vector from another velocity vector,the result is

A taxicab moves five blocks due north,six blocks due east,and another three blocks due north.Assume all blocks are of equal size.What is the magnitude of the taxi's displacement,start to finish? ​

The first displacement is 8 m,and the second displacement is 4 m.They cannot add together to give a total displacement of: ​

Vector Is 2 m long,and vector Is 4 m long.The length of the sum of the vectors must be ​

When we add a displacement vector to another displacement vector,the result is

A hiker walks 200 m west and then walks 100 m north.In what direction is her resulting displacement?

Vector Points north,and vector Points east.If=−,then vector11ec8726_cf4b_540b_8f60_37bcf0a2cf5d_TB34225555_11 Points

Which type of quantity is characterized by both magnitude and direction?

An object moves at a constant velocity of 16 m/s to the southwest for an interval of 30 s.Halfway through this interval,what is the magnitude of its instantaneous velocity?

The following force vectors act on an object: i) 55.0 newtons at 45.0° north of east and ii) 25.0 newtons at 30.0° south of east.Which of the following represents the magnitude of the resultant and its angle relative to the easterly direction?

Find the resultant of the following two vectors: i) 40 units due east and ii) 100 units 30° north of west.

A taxicab moves five blocks due north,six blocks due east,and another three blocks due north.Assume all blocks are of equal size.What is the magnitude of the taxi's displacement,start to finish?

The first displacement is 8 m,and the second displacement is 4 m.They cannot add together to give a total displacement of:

Vector Is 2 m long,and vector Is 4 m long.The length of the sum of the vectors must be