Grade 10 Physical Sciences · Mechanics

Find a resultant in one dimension

Add vectors that lie along one straight line to find the resultant and its direction (5 N east plus 3 N west gives 2 N east).

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Resultant vector | Vector addition: Grade 10 PhysicsMiss Martins Maths and Science

Representing Vectors: Head to Tail Diagrams Grade 10 PhysicsMiss Martins Maths and Science

Vectors in one dimension | Physical Science Grade 10Mayfair Academy

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Question 1.2 · November 2025 · Paper 1 · Provincial · 2 marks

Various options are provided as answers to the following questions. Choose the answer and write only the letter (A–D) next to the question numbers (1.1 to 1.10) in your ANSWER BOOK, for example, 1.11 D.

1.2 Two forces,

F_{1}

and

F_{2}

, act on a point. If

F_{1}

and

F_{2}

act in the same direction, the maximum resultant has a magnitude of

13

N. If forces

F_{1}

and

F_{2}

act in opposite directions the magnitude of the minimum resultant force is

7

N. The magnitude of the two forces, in newton, is ...(2)

A $10$ and $5$
B $16$ and $10$
C $3$ and $10$
D $8$ and $5$

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More past paper questions: find a resultant in one dimension

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3. Question WE5 · Siyavula Grade 10 Physical Sciences, 20.4 Techniques of vector addition, Worked example 5 · 3 marks
WE5 A tennis ball is rolled towards a wall which is $10$ m away from the ball. If after striking the wall the ball rolls a further $2, 5$ m along the ground away from the wall, calculate algebraically the ball's resultant displacement.(3)
Show the memo (3 ticks)Memo
1. ✓
  Positive direction and vectorsChoose towards the wall as positive.
  $x_{1} = + 10, 0 m$
  $x_{2} = - 2, 5 m$
  1 mark · Find a resultant in one dimension
2. ✓
  Add the vectors $x_{R} = x_{1} + x_{2} = (+ 10, 0 m) + (- 2, 5 m) = + 7, 5 m$
  1 mark · Find a resultant in one dimension
3. ✓
  Resultant with direction $x_{R} = 7, 5$ m towards the wall
  1 mark · Find a resultant in one dimension
4. Question WE6 · Siyavula Grade 10 Physical Sciences, 20.4 Techniques of vector addition, Worked example 6 · 3 marks
WE6 Suppose that a tennis ball is thrown horizontally towards a wall at an initial velocity of $3$ m·s $^{- 1}$ to the right. After striking the wall, the ball returns to the thrower at $2$ m·s $^{- 1}$ . Determine the change in velocity of the ball.(3)
Show the memo (3 ticks)Memo
1. ✓
  Change in velocity and signs $Δ v = v_{f} - v_{i}$
  Choose towards the wall as positive: $v_{i} = + 3$ m·s $^{- 1}$ , $v_{f} = - 2$ m·s $^{- 1}$
  1 mark · Find a resultant in one dimension
2. ✓
  Subtract the vectors $Δ v = (- 2) - (+ 3) = - 5$ m·s $^{- 1}$
  1 mark · Find a resultant in one dimension
3. ✓
  Answer with direction $Δ v = 5$ m·s $^{- 1}$ away from the wall
  1 mark · Find a resultant in one dimension
5. Question WE3 · Siyavula Grade 10 Physical Sciences, 20.4 Techniques of vector addition, Worked example 3 · 4 marks
WE3 A car breaks down in the road and you and your friend, who happen to be walking past, help the driver push-start it. You and your friend stand together at the rear of the car. If you push with a force of $50$ N and your friend pushes with a force of $45$ N, what is the resultant force on the car? Use the head-to-tail technique to calculate the answer graphically.(4)
Show the memo (4 ticks)Memo
1. ✓
  Scale and positive directionChoose the direction to the right as the positive direction. Scale: $1$ cm $= 10$ N.
  1 mark · Find a resultant in one dimension
2. ✓
  First vectorDraw your force as an arrow pointing to the right, $5$ cm long ( $50 N = 5 \times 10$ N).
  1 mark · Find a resultant in one dimension
3. ✓
  Second vector head to tailStarting at the arrowhead of the first vector, draw your friend's force pointing to the right, $4, 5$ cm long.
  1 mark · Find a resultant in one dimension
4. ✓
  ResultantDraw the resultant from the tail of the first vector to the head of the second. It measures $9, 5$ cm, so the resultant force is $95$ N to the right (in the positive direction).
  1 mark · Find a resultant in one dimension
6. Question WE6 · Siyavula Grade 11 Physical Sciences, 1.2 Resultant of perpendicular vectors, Worked example 6 · 4 marks
WE6 Given the following three force vectors, determine the resultant force:
- $F_{1} = 3, 4$ N in the positive $x$ -direction
- $F_{2} = 4$ N in the positive $x$ -direction
- $F_{3} = 3$ N in the negative $y$ -direction(4)
Show the memo (4 ticks)Memo
1. ✓
  Resultant in the x-direction $F_{1}$ and $F_{2}$ lie along the $x$ -axis, so add them tail-to-head:
  $R_{x} = 3, 4 + 4 = 7, 4$ N in the positive $x$ -direction
  1 mark · Find a resultant in one dimension
2. ✓
  Resultant in the y-directionThere is only one vector in the $y$ -direction, so $R_{y} = F_{3} = 3$ N in the negative $y$ -direction.
  1 mark · Find a resultant in one dimension
3. ✓
  Magnitude of the resultantDraw $R_{x}$ ( $7, 4$ cm) and then $R_{y}$ ( $3$ cm) head-to-tail with a scale of $1$ N : $1$ cm; the resultant runs from the tail of $R_{x}$ to the head of $R_{y}$ .
  $R = 8, 0$ N (by measurement; Pythagoras gives $7, 4^{2} + 3^{2} = 8, 0$ N)
  1 mark · Find resultant of perpendicular vectors
4. ✓
  DirectionThe angle between the resultant and the $x$ -axis is $22°$ (measured with a protractor; $tan^{- 1} \frac{3}{7 , 4} = 22°$ ).
  $R$ is $8, 0$ N at $- 22°$ from the positive $x$ -direction.
  1 mark · Find resultant of perpendicular vectors

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