Question 1

The first displacement is 6 m and the second displacement is 3 m.They cannot add together to give a total displacement of:
A)2 m.
B)3 m.
C)6 m.
D)9 m.

Accepted Answer

Displacement is a vector quantity that has both magnitude and direction. When two displacements are in opposite directions, they subtract from each other rather than adding. Therefore, the total displacement cannot be equal to the magnitude of either displacement taken alone, in this case, 6m or 3m. The only option that is not equal to either of the given displacements is 2m, so the correct answer is A.

Question 2

Vector  points north and vector  points east.If  =  -  , then vector  points:
A)north of east.
B)south of east.
C)north of west.
D)south of west.

Accepted Answer

B

Question 3

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?
A)sine
B)cosine
C)tangent
D)cotangent

Accepted Answer

B

Question 4

Which of the following is an example of a vector quantity?
A)velocity
B)temperature
C)volume
D)mass

Accepted Answer

Velocity is a vector quantity because it has both magnitude (speed) and direction (which way it's going). Temperature, volume, and mass are scalar quantities, meaning they only have magnitude.

Question 5

A taxicab moves five blocks due north, five blocks due east, and another two blocks due north.Assume all blocks are of equal size.What is the magnitude of the taxi's displacement, start to finish?
A)12 blocks
B)9.8 blocks
C)9.2 blocks
D)8.6 blocks

Accepted Answer

We can represent the taxi's movement as a vector sum. Moving five blocks due north is represented by a vector of magnitude 5 pointing directly upwards. Moving five blocks due east is represented by a vector of magnitude 5 pointing directly to the right. Moving two blocks due north is represented by a vector of magnitude 2 pointing directly upwards.

We can then add these vectors head-to-tail to find the resulting displacement vector. This can be done by drawing the vectors to scale, with the tail of each vector starting at the head of the previous vector. The resulting displacement vector will start at the beginning of the first vector and end at the end of the final vector.

The displacement vector is the diagonal of the parallelogram formed by the three vectors. Using the Pythagorean theorem, we can find the magnitude of this diagonal, which is the magnitude of the displacement vector:

magnitude = sqrt((5+2)^2 + 5^2) = sqrt(49 + 25) = sqrt(74) ≈ 8.6

Therefore, the magnitude of the taxi's displacement, start to finish, is 8.6 blocks. The correct answer is D.

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:
A)60$\degree$.
B)90$\degree$.
C)180$\degree$.
D)No maximum exists.

Accepted Answer

The answer of When three vectors are added graphically and...

Question 7

A student adds two vectors with magnitudes of 200 and 40.Which one of the following is the only possible choice for the magnitude of the resultant?
A)100
B)200
C)260
D)40

Accepted Answer

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

Question 8

The following force vectors act on an object: i) 50.0 newtons at 45.0$\degree$north of east and ii) 25.0 newtons at 30.0$\degree$south of east.Which of the following represents the magnitude of the resultant and its angle relative to the easterly direction?
A)75.0 newtons 7.50$\degree$
B)61.4 newtons 21.8$\degree$
C)23.4 newtons 18.3$\degree$
D)12.8 newtons 37.5$\degree$

Accepted Answer

To find the resultant force vector, we need to use vector addition. We can break the given force vectors into their x and y components.

For the first force vector (50.0 N at 45.0° north of east): 
Fx = 50.0 N cos(45.0°) = 35.4 N east
Fy = 50.0 N sin(45.0°) = 35.4 N north

For the second force vector (25.0 N at 30.0° south of east): 
Fx = 25.0 N cos(150.0°) = -21.7 N east
Fy = 25.0 N sin(150.0°) = -12.5 N south

Now we can add the x and y components separately:
Rx = 35.4 N east - 21.7 N east = 13.7 N east
Ry = 35.4 N north - 12.5 N south = 22.9 N north

To find the magnitude of the resultant vector R, we use the Pythagorean theorem: 
|R| = sqrt(Rx^2 + Ry^2) = sqrt(13.7^2 + 22.9^2) = 26.2 N

To find the angle of the resultant vector R relative to the easterly direction, we use the inverse tangent: 
θ = tan^-1(Ry/Rx) = tan^-1(22.9/13.7) = 59.4°

Therefore, the magnitude of the resultant and its angle relative to the easterly direction is B) 61.4 newtons 21.8°.

Question 9

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?
A)northeast
B)northwest
C)west
D)north of west

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 10

When we add a displacement vector to another displacement vector, the result is:
A)a velocity.
B)an acceleration.
C)another displacement.
D)a scalar.

Accepted Answer

When we add two displacement vectors, the resulting vector is also a displacement vector. It represents the net displacement from the initial position to the final position. Vectors cannot be added to scalars, so option D is not correct. Adding two displacements does not result in a velocity or acceleration, so options A and B are also not correct.

Question 11

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?
A)sine
B)cosine
C)tangent
D)cotangent

Accepted Answer

The x-component of a vector is equal to the magnitude of the vector multiplied by the cosine of the angle between the vector and the x-axis. This can be represented as x = ||v||cosθ. Thus, the correct choice is B) cosine.

Question 12

A hiker walks 200 m west and then walks 100 m north.In what direction is her resulting displacement?
A)north
B)west
C)northwest
D)None of the answers is correct.

Accepted Answer

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

Question 13

An object moves at a constant velocity of 11 m/s to the southwest for an interval of 20 s.Halfway through this interval, what is the magnitude of its instantaneous velocity?
A)It can be any value from 0 to 22 m/s.
B)11 m/s
C)5.5 m/s
D)More information is needed.

Accepted Answer

The answer of An object moves at a constant velocity...

Question 14

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)dividing by cosine
B)dividing by sine
C)multiplying by cosine
D)multiplying by sine

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 15

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)1^st B)2^nd C)3^rd D)None, since the object is now moving in the y-direction.

Accepted Answer

Since the object started in the negative x-direction and then experienced a change in velocity in the positive y-direction, the resulting velocity vector points in the second quadrant (negative x-axis, positive y-axis).

Question 16

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:
A)occurs one-fourth of the way around the track.
B)occurs one-half of the way around the track.
C)occurs three-fourths of the way around the track.
D)Both a and c are correct.

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 17

When we subtract a velocity vector from another velocity vector, the result is:
A)another velocity.
B)an acceleration.
C)a displacement.
D)a scalar.

Accepted Answer

When we subtract a velocity vector from another velocity vector, the result is another velocity vector. This new velocity vector represents the change in velocity between the initial and final velocities.

Question 18

Find the resultant of the following two vectors: i) 50 units due east and ii) 100 units 30$\degree$ north of west.
A)100 units 30$\degree$ north of west
B)62 units 15$\degree$north of west
C)87 units 60$\degree$north of west
D)62 units 54$\degree$ north of west

Accepted Answer

The answer of Find the resultant of the following two...

Question 19

Which type of quantity is characterized by both magnitude and direction?
A)scalar
B)vector
C)trigonometric
D)algebraic variable

Accepted Answer

Vectors are characterized by both magnitude (size) and direction. Scalars, on the other hand, only have magnitude. Trigonometric and algebraic variables do not necessarily have a direction component.

Question 20

Vector  is 3 m long and vector  is 4 m long.The length of the sum of the vectors must be:
A)5 m.
B)7 m.
C)12 m.
D)some value from 1 m to 7 m.

Accepted Answer

The answer of Vector  is 3 m long and...

Quiz 3: Vectors and Two-Dimensional Motion

The first displacement is 6 m and the second displacement is 3 m.They cannot add together to give a total displacement of:

Vector points north and vector points east.If = - , then vector points:

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?

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

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

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:

A student adds two vectors with magnitudes of 200 and 40.Which one of the following is the only possible choice for the magnitude of the resultant?

The following force vectors act on an object: i) 50.0 newtons at 45.0 $\degree$ north of east and ii) 25.0 newtons at 30.0 $\degree$ south of east.Which of the following represents the magnitude of the resultant and its angle relative to the easterly direction?

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?

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

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?

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

An object moves at a constant velocity of 11 m/s to the southwest for an interval of 20 s.Halfway through this interval, what is the magnitude of its instantaneous velocity?

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)

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 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:

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

Find the resultant of the following two vectors: i) 50 units due east and ii) 100 units 30 $\degree$ north of west.

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

Vector is 3 m long and vector is 4 m long.The length of the sum of the vectors must be: