Grade 12 Physical Sciences · Mechanics · Solve for two objects moving vertically

Solve for two objects moving vertically Grade 12

Write the position of each object in terms of time and set them equal to find when and where they meet, or subtract them to find how far apart they are.

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3a) Vertical projectile motion | two objectsKevinmathscience

Vertical Projectile Motion Two Objects Exam QuestionMiss Martins Maths and Science

3) Grade 12 Physics: Vertical Projectile Motion: Two Objects – Finding When and Where They Meet.Sir Mike Maths & Science Club

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Question 3.3 · May/June 2022 · Paper 1 · National (DBE) · 6 marks

A small disc, C, is thrown vertically upwards at a speed of

15

m·s

^{- 1}

from the edge of the roof of a building of height

30

m. AFTER

0, 5

s, a small ball B is shot vertically upwards from the foot of the building at a speed of

40

m·s

^{- 1}

in order to hit disc C, as shown in the diagram below.

Ignore the effects of air resistance. Diagram for this question

3.3 Calculate the time from the moment that disc C was thrown upwards until the time ball B hits the disc.(6)

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

More past paper questions: solve for two objects moving vertically

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3. Question 3.1.1 · November 2024 · Paper 1 · National (DBE) · 5 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:
3.1.1 t(5)
Show the memo (5 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 for ball A $Δ y = 12 t + \frac{1}{2} (- 9, 8) t^{2}$ ...... Eqn (1)
  1 mark · Use equations of motion for projectiles
3. ✓
  Substitution for ball B $Δ y = - 5, 4 (t - 2) + \frac{1}{2} (- 9, 8) (t - 2)^{2}$ ...... Eqn (2)
  1 mark · Use equations of motion for projectiles
4. ✓
  Equate displacements $Δ y_{A} = Δ y_{B}$ :
  $12 t + \frac{1}{2} (- 9, 8) t^{2} = - 5, 4 (t - 2) + \frac{1}{2} (- 9, 8) (t - 2)^{2}$
  1 mark · Solve for two objects moving vertically
5. ✓
  Answer $12 t = - 5, 4 t + 10, 8 - 19, 6 + 19, 6 t$
  $t = 4$ (s)
  1 mark · Use equations of motion for projectiles
4. Question 3.2.2 · May/June 2023 · Paper 1 · National (DBE) · 5 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:
3.2.2 Magnitude of the velocity with which ball B was projected from the ground(5)
Show the memo (5 ticks)Memo
1. ✓
  Formula (time for A to fall 3,2 m)Upwards 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 for ball A $- 3, 2 = (0) + \frac{1}{2} (- 9, 8) (Δ t)^{2}$
  $Δ t = 0, 81$ s
  1 mark · Use equations of motion for projectiles
3. ✓
  Subtraction 1,76 − 0,81 $Δ t (B) = 1, 76 - 0, 81$
  $Δ t (B) = 0, 95$ s
  1 mark · Solve for two objects moving vertically
4. ✓
  Substitution for ball B $Δ y = v_{i} Δ t + \frac{1}{2} a Δ t^{2}$
  $(0) = v_{i} (0, 95) + \frac{1}{2} (- 9, 8) (0, 95)^{2}$
  1 mark · Use equations of motion for projectiles
5. ✓
  Answer with unit $v_{i} = 4, 66$ m·s $^{- 1}$
  1 mark · Use equations of motion for projectiles
5. Question 3.2.3 · September 2026 · Paper 1 · Provincial · 4 marks
An object, A, is dropped from a certain height h above the ground. At EXACTLY THE SAME TIME, object B is thrown upwards from the ground. They pass each other after exactly 1,5 seconds. Object B hits the ground 3,5 seconds after being projected upwards.
3.2 Calculate the:
3.2.3 Height h above the ground from which A is dropped(4)
Show the memo (4 ticks)Memo
1. ✓
  FormulaDistance A travelled from rest in $1, 5$ s:
  $Δ y = v_{i} Δ t + \frac{1}{2} a Δ t^{2}$
  1 mark · Use equations of motion for projectiles
2. ✓
  Substitution $Δ y = 0 + \frac{1}{2} (9, 8) (1, 5)^{2} = 11, 025$ m
  1 mark · Use equations of motion for projectiles
3. ✓
  Adding the passing heightTotal height $= 11, 025 + 14, 7$
  1 mark · Solve for two objects moving vertically
4. ✓
  Answer $h = 25, 725$ m ( $25, 73$ m)
  1 mark · Use equations of motion for projectiles
6. Question 3.2.1 · September 2026 · Paper 1 · Provincial · 5 marks
Ball L is thrown vertically upwards from the ground with an initial velocity v. At the same moment, a second ball, K, is dropped from rest from a balcony $20$ m above the ground. The two balls pass one another after $1, 2$ s.
3.2 Use only equations of motion and calculate:
3.2.1 The magnitude of the initial velocity of ball L as it is thrown upwards(5)
Show the memo (5 ticks)Memo
1. ✓
  FormulaDown as positive.
  Ball K:
  $Δ y = v_{i} Δ t + \frac{1}{2} a Δ t^{2}$
  1 mark · Use equations of motion for projectiles
2. ✓
  Substitution for ball K $Δ y = (0) (1, 2) + \frac{1}{2} (9, 8) (1, 2)^{2}$
  $= 7, 056$ m
  1 mark · Use equations of motion for projectiles
3. ✓
  Displacement of ball LBall L:
  $Δ y = v_{i} Δ t + \frac{1}{2} a Δ t^{2}$
  $Δ y_{L} = - (20 - 7, 056)$
  1 mark · Solve for two objects moving vertically
4. ✓
  Substitution for ball L $- (20 - 7, 056) = v_{i} (1, 2) + \frac{1}{2} (9, 8) (1, 2)^{2}$
  1 mark · Use equations of motion for projectiles
5. ✓
  Answer $v_{i} = - 16, 667$ m·s $^{- 1}$
  $v_{i} = 16, 67$ m·s $^{- 1}$
  1 mark · Use equations of motion for projectiles

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