Grade 12 Physical Sciences · Mechanics

Use equations of motion for projectiles

Use equations of motion with a = g for objects thrown up or dropped, for example finding the maximum height of a ball thrown up at 10 m/s.

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1) Vertical projectile motion introductionKevinmathscience

2) Vertical projectile motion calculationsKevinmathscience

3a) Vertical projectile motion | two objectsKevinmathscience

Grade 12 Vertical Projectile Motion: Introduction: Gr 12 PhysicsMiss Martins Maths and Science

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Question 3.2 · May/June 2025 · Paper 1 · National (DBE) · 4 marks

A ball is dropped from point A and reaches point B h metres below point A, in time t. The ball takes

2

s to fall from point B to point C on the ground. The distance from point B to point C is 8h metres. See the diagram below.

Ignore the effects of air friction. Diagram for this question

3.2 Show, by means of calculations, that time t is equal to 1 second.(4)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: use equations of motion for projectiles

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3. Question 3.1.2 · November 2024 · Paper 1 · National (DBE) · 3 marks
Ball A is thrown vertically upwards at $12$ m·s $^{- 1}$ from the top of a building. Two seconds after ball A was thrown upwards, ball B is thrown vertically downwards at $5, 4$ m·s $^{- 1}$ from the top of the same building. Both balls, A and B, strike the ground at time t seconds.

Ignore the effects of air friction.

The position-time sketch graphs for both balls are shown below.
3.1 Using EQUATIONS OF MOTION ONLY, calculate the value of EACH of the following, as shown in the graphs:
3.1.2 Z(3)
Show the memo (3 ticks)Memo
1. ✓
  FormulaUpwards as positive, ball A:
  $Δ y = v_{i} Δ t + \frac{1}{2} a Δ t^{2}$
  1 mark · Use equations of motion for projectiles
2. ✓
  Substitution $Δ y = (12) (4) + \frac{1}{2} (- 9, 8) (4)^{2}$
  1 mark · Use equations of motion for projectiles
3. ✓
  Answer $Δ y = - 30, 4$ m
  $Z = 30, 4$ (m)
  1 mark · Use equations of motion for projectiles
4. Question 3.3.1 · May/June 2024 · Paper 1 · National (DBE) · 3 marks
A hot-air balloon moves vertically downwards at a constant velocity of $3, 4$ m·s $^{- 1}$ . When the balloon is $15$ m above the ground, a small ball is dropped from the balloon. Refer to the diagram below.

The ball strikes the ground and bounces vertically upwards. The hot-air balloon continues to move downwards at the same constant velocity.

Ignore the effects of air friction acting on the ball.
3.3 Use only EQUATIONS OF MOTION to calculate:
3.3.1 The value of $t_{1}$ indicated on the graph(3)
Show the memo (3 ticks)Memo
1. ✓
  Formula with $Δ t$ Downwards as positive:
  $Δ y = v_{i} Δ t + \frac{1}{2} a Δ t^{2}$
  1 mark · Use equations of motion for projectiles
2. ✓
  Substitution $15 = 3, 4Δ t + \frac{1}{2} (9, 8) Δ t^{2}$
  1 mark · Use equations of motion for projectiles
3. ✓
  Final answer $Δ t = 1, 44$ s, so $t_{1} = 1, 44$ s
  1 mark · Use equations of motion for projectiles
5. Question 3.2.1 · May/June 2023 · Paper 1 · National (DBE) · 3 marks
Ball A is dropped from rest from the top of a building $15, 2$ m high.

After ball A has fallen $3, 2$ m, a second ball B is projected vertically upwards from the ground. After a while, the two balls strike the ground at the SAME time.

Ignore the effects of air resistance.
3.2 Calculate the:
3.2.1 Time taken for ball A to strike the ground(3)
Show the memo (3 ticks)Memo
1. ✓
  FormulaDownwards as positive:
  $Δ y = v_{i} Δ t + \frac{1}{2} a Δ t^{2}$
  1 mark · Use equations of motion for projectiles
2. ✓
  Substitution $15, 2 = (0) + \frac{1}{2} (9, 8) Δ t^{2}$
  1 mark · Use equations of motion for projectiles
3. ✓
  Answer with unit $Δ t = 1, 76$ s
  1 mark · Use equations of motion for projectiles
6. Question 2.5 · May/June 2023 · Paper 1 · National (DBE) · 5 marks
Block A of mass m is connected to block B of mass $7, 5$ kg by a light inextensible rope passing over a frictionless pulley. Block B is initially held at a height of $1, 5$ m above the ground, while block A is initially stationary on the ground, as shown in the diagram below.

When block B is released, it moves vertically downwards and strikes the ground with a velocity of $3, 41$ m·s $^{- 1}$ .

Ignore the effects of friction.
2.5 Calculate the maximum height above the ground reached by block A.(5)
Show the memo (5 ticks)Memo
1. ✓
  METHOD 1: FormulaUpwards as positive:
  $v_{f}^{2} = v_{i}^{2} + 2 a Δ y$
  1 mark · Use equations of motion for projectiles
2. ✓
  METHOD 1: Substitution of $v_{i}$ and $v_{f}$ $(0)^{2} = (3, 41)^{2} + \dots$
  1 mark · Use equations of motion for projectiles
3. ✓
  METHOD 1: Substitution of g $(0)^{2} = (3, 41)^{2} + (2) (- 9, 8) Δ y$
  $Δ y = 0, 59$ m
  1 mark · Use equations of motion for projectiles
4. ✓
  METHOD 1: Adding 1,5 mMaximum height $= 0, 59 + 1, 5$
  1 mark · Use equations of motion for projectiles
5. ✓
  METHOD 1: Answer with unit $= 2, 09$ m
  1 mark · Use equations of motion for projectiles

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