The velocity vectors vX and vY of two cars, X and Y, are shown.
Which arrow represents the direction of the vector vX – vY?
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Syllabus Edition
First teaching 2014
Last exams 2024
The velocity vectors vX and vY of two cars, X and Y, are shown.
Which arrow represents the direction of the vector vX – vY?
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Which of the following statements about scalar quantities is incorrect?
Scalar quantities contain a magnitude only
Mass is a scalar quantity
Scalar quantities contain both magnitude and direction
Speed is a scalar quantity
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Which of the following quantities is not a vector?
Acceleration
Weight
Mass
Drag
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A vector of magnitude 10 units is shown with respect to a set x and y axes.
What is the correct expression for the components of the vector along the x and y axis?
Component along the x axis | Component along the y axis | |
A. | 10 cos 76 | 10 sin 76 |
B. | 10 cos 76 | 10 sin 14 |
C. | 10 sin 76 | 10 cos 76 |
D. | 10 sin 76 | 10 cos 14 |
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A vector P has components Px = 3.0 cm and Py = 4.0 cm.
What is the length of the vector P?
1.0 cm
5.0 cm
7.0 cm
25.0 cm
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Three forces act on a body in equilibrium. Which diagram is a possible vector diagram for this situation?
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Three forces act on a body as shown:
Which of the following statements is correct?
The body is in equilibrium
The force required to bring the body into equilibrium is directed in a north west direction
The force required to bring the body into equilibrium is directed in a south east direction
There is no resultant force on the body
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Which of the following units is used to measure vectors only?
m
m s–1
s
N
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Which of the following units is used to measure scalar quantities only?
s
m
m s–1
m s–2
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Which of the following statements about vector quantities is incorrect?
Vectors quantities include a magnitude
Vector quantities contain a direction
Vector quantities are only positive
Vector quantities are positive or negative
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Velocity is a vector quantity, so can be represented by a vector arrow. Which quantity is represented by the length of its vector arrow?
Speed
Magnitude
Acceleration
Distance
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Which of the following represents correct vector and scalar quantities?
|
vectors |
scalars |
A. |
Electric charge |
Weight |
B. |
Impulse |
Current |
C. |
Temperature |
Pressure |
D. |
Time |
Work done |
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Which of the following represents the correct values of the x-component and y-component of the vector -F ?
|
x-component |
y-component |
A. |
–F sin θ |
–F cos θ |
B. |
–F cos θ |
–F tan θ |
C. |
F sin θ |
–F cos θ |
D. |
–F cos θ |
–F sin θ |
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The magnitude of a is 15 N and that of b is 30 N.
Which of the following represents the correct resultant horizontal and vertical components of the vectors in the diagram?
|
Horizontal Component |
Vertical Component |
A. |
15 – 7.5N |
15 – 7.5N |
B. |
15 – 7.5º |
–15 – 7.5º |
C. |
15 – 7.5N |
–15 – 7.5N |
D. |
–15 – 7.5 N |
15 – 7.5 N |
You may use the fact that:
cos(30) = and cos(45) =
sin(30) = and sin(45) =
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The diagram shows vector p.
In which of the following diagrams is vector p multiplied by a scalar represented?
1 and 4
2 only
2 and 4
1 only
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In which of the following diagrams is the addition of vectors x and y represented?
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In which of the following diagrams is q – p represented correctly?
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The arrow represents the vector R.
Which diagram does not represent R as two perpendicular components?
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Three forces act on a body as shown.
Which fourth force is required so that the resultant force is zero?
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A rectangular object sits at rest on a plane inclined at angle to the horizontal.
R is the normal force, W is the weight and F is friction.
Which row correctly labels R and F in terms of mass m and acceleration due to gravity g.
|
R |
F |
A. |
mg |
mg |
B. |
mg cos θ |
0 |
C. |
mg sin θ |
mg cos θ |
D. |
mg cos θ |
mg sin θ |
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A pilot wishes to set her plane on a course such that it flies directly west of its starting point. She must take into account the strong northerly wind, meaning that she is flying in a wind which originates in the north and blows in a southward direction.
On which course should the plane be directed?
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A positron is in the effect of two electric fields, shown measured in arbitrary units.
What is the magnitude of the resultant field strength on the positron?
You may use any of the following results:
V m–1
6 V m–1
13 V m–1
V m–1
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A drifting spider of mass 50 g hangs on its web from point P on a ceiling. It is being displaced at an angle θ to the vertical by a gentle breeze equivalent to 0.2 N.
What is the magnitude of the angle θ?
You may assume g = 10 m s–2
sin–1 (0.4)
cos–1 (2.5)
tan–1 (0.4)
tan–1 (2.5)
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A horizontal force F accelerates a body of mass m up a rough plane inclined at an angle θ to the horizontal.
Which expression describes the magnitude of the resultant force on the body?
F cos θ – mg sin θ
F cos θ – mg (sin θ – μd cos θ)
F(cos θ – μd sin θ) – mg (sin θ – μd cos θ)
mg (sin θ – μd cos θ) + F(cos θ – μd sin θ)
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A box rests on an inclined plane.
Which of the following statements is correct if the incline becomes less steep?
Vector Y decreases
Vector Y increases
Vector X increases
Vector Z increases
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The following processes are given:
Which of the processes is a scalar quantity?
I and II only
III only
II and III only
I, II and III
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Alice sits on the platform of a train station, observing the trains as they move past, from left to right, at constant velocity.
Bob is sat in one particular train carriage, and throws a tennis ball vertically upward, catching it as it comes back down.
Which diagram best represents the trajectory of the tennis ball relative to Alice? (Note: this is the path the ball will follow relative to Alice's position, not what she will see.)
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In some models of quantum theory, photons of light take infinitely many paths between two points P and Q in space. Three such paths are shown.
We can associate a mathematical object called a phasor to each of these unique paths. A phasor can be thought of as a spinning vector. For example, when a photon leaves its source P, its associated phasor begins rotating like a clock, until the photon is detected at Q. At this instant, the phasor stops rotating.
In this way, different paths are represented by different phasors. The phasor's final orientation depends on the time taken by the photon to travel between P and Q.
Some example final positions of phasors for different paths are shown:
Quantum theory requires that phasors for every possible path are used to calculate the probability of detecting a photon at Q. More specifically, the probability of detecting a photon at Q is proportional to the square of the resultant phasor amplitude at Q.
Which diagram best represents the resultant phasor amplitude at Q if Q is the dark fringe of an interference pattern?
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A car drives from its base camp, at position X, to lodge P, 40 km away, at a bearing of 030° from X. After dropping off supplies it continues to lodge Q, which is 50 km away and at a bearing of 330° from P.
What is the distance between base camp and lodge Q?
You may use one, none or some of the following values for cosines in your calculation:
cos(60) = + 0.5
cos(90) = 0
cos(120) = − 0.5
km
km
km
km
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A vector field is a mathematical description which assigns a vector to every point in a subset of space.
Which of the following vector fields could not be represented by the image shown?
A gravitational vector field
An electric vector field
A velocity vector field
A magnetic vector field
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