ASPhysicsCIETopic Questions1. Physical Quantities & Units1.4 Scalars & Vectors

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First teaching 2023

First exams 2025

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Scalars & Vectors (CIE AS Physics)

Topic Questions

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1a
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Distinguish between scalar and vector quantities.

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1b
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(i)

Energy is a scalar quantity. State three other scalar quantities.

[3]
(ii)
Force is a vector quantity. State three other vector quantities.
[3]

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1c
Sme Calculator4 marks

Fig. 1.1 shows a block at rest on a slope.

Three forces, weight W, normal contact force N and the frictional force F act on the block. The forces are in equilibrium.

1-1-1c-e-1-1-e-box-slope-vector-combine-cie-ial-sq

(i)
Explain what is meant by 'the forces are in equilibrium'.
[2]
(ii)
Complete the vector triangle in Fig. 1.2. Label the missing vector and the angle between W and N.
 

1-1-1c-e-1-1-e-box-slope-vector-triangle-cie-ial-sq

[2]

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1d
Sme Calculator4 marks

The frictional force has a magnitude of 60 N.

By resolving the vector, calculate the component of the force that acts

 
(i)
horizontally
[2]
(ii)
vertically.
[2]

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2a
Sme Calculator2 marks

State the definition of a vector quantity. 

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2b
Sme Calculator3 marks

A list of vector quantities and their SI unit is given.

Quantity SI unit
Temperature  
  kg m s-1
Mass  

Complete the information missing from the table. 

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2c
Sme Calculator2 marks

A person cycles along a path every day, from their front garden at X to a bench by the nearby lake at Y, as shown in Fig. 1.1.

1-3-q1c-easy-sq-sl-phy

Fig. 1.1

(i)
Sketch a line on the image that would indicate the distance travelled by the person between X and Y. Label this distance d. 
[1]
(ii)
State whether the distance travelled d by the person is greater than, equal to, or less than their displacement between X and Y.
[1]

 

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2d
Sme Calculator2 marks

The person continues their journey and walks along the same path back home, from Y to X. The total distance for their complete journey which was logged by their smartwatch is 4.3 km. State and explain what the total displacement for their journey is. 

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3a
Sme Calculator2 marks

A small cannon fires a projectile at an angle of 22° to the horizontal with an initial velocity v. 

1-3-q4a-easy-sq-sl-phy

Calculate the vertical component of velocity if its initial velocity has a magnitude of v = 15 m s–1. 

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3b
Sme Calculator1 mark

State the direction of the horizontal component of velocity. 

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3c
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The cannon fires a second projectile. The initial horizontal component of velocity is 8.4 m s-1 and the initial vertical component of velocity is 5.8 m s-1.

Calculate the initial velocity, v2, of the second projectile.

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3d
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Calculate the angle to the horizontal that the second projectile was fired at.

[2]

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1a
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Fig. 1.1 shows two taut, light ropes that keep a pole vertically upright by applying two tension forces, one of magnitude 200 N and one of magnitude T. 

sl-sq-1-3-hard-q3a

Fig. 1.1

By constructing a scale diagram, determine the weight of the pole W and the magnitude of T. 

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1b
Sme Calculator3 marks

A canoeist can paddle at a speed of 3.8 m s–1 in still water. The canoeist encounters an opposing current, moving at a speed of 1.5 m s–1 at 30° to their original direction of travel, as shown in Fig. 1.2. 

sl-sq-1-3-hard-q3b

Fig. 1.2

Using Fig. 1.2 to construct a scale diagram, determine the magnitude of the canoeist's resultant velocity. 

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1c
Sme Calculator4 marks

The boat shown in Fig. 1.3 is being towed at a constant velocity by a towing rope, which exerts a tension force FT = 2500 N.

There are two resistive forces indicated; the force of the water on the keel FK and the force of the water on the rudder, FR. 

sl-sq-1-3-hard-q3c

Fig. 1.3

By scale diagram or otherwise, determine the magnitude of FR. 

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1d
Sme Calculator4 marks

Another boat wishes to cross a river. The river flows from west to east at a constant velocity of 35 cm s–1 and the boat leaves the south bank, due north, at 1.5 m s–1 as shown in Fig. 1.4.

sl-sq-1-3-hard-q3d

Fig. 1.4

Construct a scale diagram to show that the new direction of the boat is about 13° East of North.

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2a
Sme Calculator3 marks

A plane flying across the Lake District sets off from base camp to Lake Windermere, 28 km away, in a direction of 20.0° north of east. 

After dropping off supplies it flies to Lake Coniston, which is 19 km at 30.0° west of north from Lake Windermere. 

By constructing a scale drawing, determine the distance from Lake Coniston to base camp. 

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2b
Sme Calculator2 marks

The plane now flies due north with a speed v. It moves through air that is stationary relative to it. 

sl-sq-1-3-hard-q2b

Suddenly, the plane enters a region where the wind is blowing with a speed u from a direction of θ anticlockwise from south.

Determine an expression for the time taken t for the plane to fly a distance D due north of its current position in this windy region. 

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2c
Sme Calculator3 marks

In still air, the plane travels 180 km every 30 minutes. In the windy region described in part (c), the aircraft takes an extra 4 minutes to travel the same distance, when the wind blows at an angle 53° anticlockwise from south. 

Assuming the orientation of the plane does not change, calculate the speed of the wind u in km h–1. 

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2d
Sme Calculator3 marks

The wind now blows due south with the same speed as in part (c). The plane continues to travel at the same speed in this windy region. 

sl-sq-1-3-hard-q2d

The pilot wishes to cross the sky along the straight line AB. In order to do so, they must turn the plane at an angle φ clockwise from north. 

Construct a scale drawing to determine φ. 

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1a
Sme Calculator7 marks

The relationship can be used to model a spherical raindrop falling vertically in the air.

Fig 1.1 shows the forces acting on the raindrop as it accelerates downwards.

1-1-3c-m-1-1-raindrop-sphere-vector-forces-cie-ial-sq

The raindrop has a radius of 1.5 mm and falls at a velocity of 3.5 m s−1. The constant k has a magnitude of 0.0124 in air.

Other than the resistive force F described in (b), two other forces, X and Y, act on the raindrop drop as it falls through the air. 

(i)
State the names of forces X and Y.
[2]

  

(ii)
Calculate the magnitude of the resistive force F in µN.
[2]
 
(iii)
Force X has a value of 137 µN and force Y has a value of 0.18 µN.
 
Using Fig. 1.1, determine the magnitude and direction of the resultant force on the raindrop.
[3]

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1b
Sme Calculator3 marks

On a windy day, the resultant force on the raindrop is 105 µN at an angle of θ to the vertical as shown in Fig. 1.2. 

1-1-3d-m-1-1-raindrop-sphere-vector-angle-cie-ial-sq

Use your answer to (c)iii to show that the angle θ between the resultant and the vertical is about 47°.

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2a
Sme Calculator2 marks
(i)
State the difference between a scalar quantity and a vector quantity.
[1]
(ii)
Underline all the vectors in the list below.
 
power           length           density           velocity           momentum
[1]

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2b
Sme Calculator4 marks

Two gusts of wind exert forces of magnitude 5.5 N and 11.9 N on a wind turbine at a point O. Both forces act away from point O and the angle between them is 30°.

Fig. 1.1 shows two lines at an angle of 30° to one another.

 

1-1-4b-m-1-1-vector-force-triangle-cie-ial-sq

Fig. 1.1

 

On Fig. 1.1, draw a vector diagram to determine the magnitude of the resultant of the two forces.

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3a
Sme Calculator4 marks

Fig. 1.1 shows a 2 tonne wrecking ball being used on a demolition site. 

1-1-5a-m-1-1-wrecking-ball-resolving-vectors-cie-ial-sq

The ball is suspended from a cable which makes an angle θ with the vertical. The ball is pulled into the position shown by a rope that is kept horizontal. The tension in the rope is 6400 N.

Write expressions for tension T using

(i)
the vertical component of the tension in the cable
[2]
(ii)
the horizontal component of the tension in the cable. 
[2]

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3b
Sme Calculator4 marks

Determine

(i)
the angle θ the cable makes with the vertical
[2]
(ii)
the magnitude of the tension T in the cable
[2]

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3c
Sme Calculator3 marks

On the same demolition site, there is a uniform beam supported by two light cables, AB and AC, which are attached to a single steel cable from a crane, as shown in Fig. 1.2.

The beam is stationary and in equilibrium.

q5c_vectors--scalars-in-physics_ib-sl-physics-sq

Fig. 1.2

Draw the vector triangle for this situation labelling the tension in both cables and the weight of the beam. 

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3d
Sme Calculator2 marks

The tension in the cable AB is 9 N and the tension in the cable AC is 12 N.

Calculate the resultant force required in the beam BC to keep the system in equilibrium.

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