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Projectiles

Past-paper questions pack

Name
Class
Date set
Date due
Score/ 92

Questions are numbered; the mark schemes (the answer key) follow on separate pages so the question pages can be handed out alone. www.mathsaleveltutor.com

Edexcel AS and A-level Maths past-paper questions since June 2018 · 29 parts, 92 marks · mark schemes follow the questions · www.mathsaleveltutor.com · Questions and mark schemes © Pearson Education Ltd

1. June 2025 · Paper 3 (Mechanics) · Q5(a) · 5 marks
5. –1 14 m s theta H m N A 40 m Figure 3 –1 from a point O on the top of a cliff. A small stone is projected with speed 14 m s The point O is H metres vertically above the point N. Point N is on horizontal ground. The stone is projected at an angle theta above the horizontal, where tan theta = 1 The stone strikes the horizontal ground at the point A, where NA = 40 m, as shown in Figure 3. The stone is modelled as a particle moving freely under gravity. Using this model, find (a) the value of H (5)
2. June 2025 · Paper 3 (Mechanics) · Q5(b) · 3 marks
(b) the maximum height of the stone above the horizontal ground. (3)
3. June 2024 · Paper 3 (Mechanics) · Q5(a) · 6 marks
5. 35 m s –1 alpha A Figure 4 At time t = 0, a small stone is projected with velocity 35 m s –1 from a point O on horizontal ground. The stone is projected at an angle alpha to the horizontal, where tan alpha = 3 In an initial model • the stone is modelled as a particle P moving freely under gravity • the stone hits the ground at the point A Figure 4 shows the path of P from O to A. For the motion of P from O to A • at time t seconds, the horizontal distance of P from O is x metres • at time t seconds, the vertical distance of P above the ground is y metres (a) Using the model, show that y x x (6)
4. June 2024 · Paper 3 (Mechanics) · Q5(b) · 2 marks
(b) Use the answer to (a), or otherwise, to find the length OA. (2)
5. June 2024 · Paper 3 (Mechanics) · Q5(c) · 2 marks
Using the model, the greatest height of the stone above the ground is found to be H metres. (c) Use the answer to (a), or otherwise, to find the value of H. (2)
6. June 2024 · Paper 3 (Mechanics) · Q5(d) · 1 marks
• The model is refined to include air resistance. Using this new model, the greatest height of the stone above the ground is found to be K metres. (d) State which is greater, H or K, justifying your answer. (1)
7. June 2024 · Paper 3 (Mechanics) · Q5(e) · 1 marks
(e) State one limitation of this refined model. (1)
8. June 2023 · Paper 3 (Mechanics) · Q5(a) · 2 marks
5. A –1 28 m s 20 m alpha 40 m Figure 2 –1 from a point O on horizontal ground. A small ball is projected with speed 28 m s After moving for T seconds, the ball passes through the point A. The point A is 40 m horizontally and 20 m vertically from the point O, as shown in Figure 2. The motion of the ball from O to A is modelled as that of a particle moving freely under gravity. Given that the ball is projected at an angle alpha to the ground, use the model to (a) show that T = 7cos alpha (2)
9. June 2023 · Paper 3 (Mechanics) · Q5(b) · 5 marks
2 alpha – 4 tan alpha + 3 = 0 (b) show that tan (5)
10. June 2023 · Paper 3 (Mechanics) · Q5(c) · 3 marks
(c) find the greatest possible height, in metres, of the ball above the ground as the ball moves from O to A. (3)
11. June 2023 · Paper 3 (Mechanics) · Q5(d) · 1 marks
The model does not include air resistance. (d) State one other limitation of the model. (1)
12. June 2022 · Paper 3 (Mechanics) · Q5(a) · 6 marks
5. alpha A B 120 m Figure 3 A golf ball is at rest at the point A on horizontal ground. The ball is hit and initially moves at an angle alpha to the ground. The ball first hits the ground at the point B, where AB = 120 m, as shown in Figure 3. The motion of the ball is modelled as that of a particle, moving freely under gravity, whose initial speed is U m s –1 Using this model, (a) show that U 2 sin alpha cos alpha = 588 (6)
13. June 2022 · Paper 3 (Mechanics) · Q5(b) · 4 marks
The ball reaches a maximum height of 10 m above the ground. (b) Show that U 2 = 1960 (4)
14. June 2022 · Paper 3 (Mechanics) · Q5(c) · 1 marks
In a refinement to the model, the effect of air resistance is included. The motion of the ball, from A to B, is now modelled as that of a particle whose initial speed is V m s –1 This refined model is used to calculate a value for V (c) State which is greater, U or V, giving a reason for your answer. (1)
15. June 2022 · Paper 3 (Mechanics) · Q5(d) · 1 marks
(d) State one further refinement to the model that would make the model more realistic. (1)
16. Oct 2021 · Paper 3 (Mechanics) · Q4(a) · 4 marks
4. 65 m s-1 alpha 70 m N A Figure 3 A small stone is projected with speed 65 m s-1 from a point O at the top of a vertical cliff. Point O is 70 m vertically above the point N. Point N is on horizontal ground. The stone is projected at an angle alpha above the horizontal, where tan alpha = 5 The stone hits the ground at the point A, as shown in Figure 3. The stone is modelled as a particle moving freely under gravity. The acceleration due to gravity is modelled as having magnitude 10 m s-2 Using the model, (a) find the time taken for the stone to travel from O to A, (4)
17. Oct 2021 · Paper 3 (Mechanics) · Q4(b) · 5 marks
(b) find the speed of the stone at the instant just before it hits the ground at A. (5)
18. Oct 2021 · Paper 3 (Mechanics) · Q4(c) · 1 marks
One limitation of the model is that it ignores air resistance. (c) State one other limitation of the model that could affect the reliability of your answers. (1)
19. Oct 2020 · Paper 3 (Mechanics) · Q5(a) · 6 marks
5. U m s-1 45° 25 m N A 100 m Figure 2 A small ball is projected with speed U m s-1 from a point O at the top of a vertical cliff. The point O is 25 m vertically above the point N which is on horizontal ground. The ball is projected at an angle of 45° above the horizontal. The ball hits the ground at a point A, where AN = 100 m, as shown in Figure 2. The motion of the ball is modelled as that of a particle moving freely under gravity. Using this initial model, (a) show that U = 28 (6)
20. Oct 2020 · Paper 3 (Mechanics) · Q5(b) · 3 marks
(b) find the greatest height of the ball above the horizontal ground NA. (3)
21. Oct 2020 · Paper 3 (Mechanics) · Q5(c) · 1 marks
In a refinement to the model of the motion of the ball from O to A, the effect of air resistance is included. This refined model is used to find a new value of U. (c) How would this new value of U compare with 28, the value given in part (a)? (1)
22. Oct 2020 · Paper 3 (Mechanics) · Q5(d) · 1 marks
(d) State one further refinement to the model that would make the model more realistic. (1)
23. June 2019 · Paper 3 (Mechanics) · Q5(a) · 6 marks
* P_20ms? ums’ 2 A 30° CIN Al 50m_____ 8 Figure 3 The points 4 and B lie 50m apart on horizontal ground. At time ¢ = 0 two small balls, P and Q, are projected in the vertical plane containing AB. Ball P is projected from A with speed 20ms" at 30° to AB. Ball Q is projected from B with speed ums" at angle @ to BA, as shown in Figure 3. At time ¢ = 2 seconds, P and Q collide. Until they collide, the balls are modelled as particles moving freely under gravity. (a) Find the velocity ofP at the instant before it collides with QO. (6)
24. June 2019 · Paper 3 (Mechanics) · Q5(b) · 6 marks
(6) (b) Find (1) the size ofangle 0, (11) the value of w.
25. June 2019 · Paper 3 (Mechanics) · Q5(c) · 1 marks
(c) State one limitation of the model, other than air resistance, that could affect the accuracy ofyour answers.
26. June 2018 · Paper 3 · Q10(a) · 2 marks
10. U alpha A 3 m 2 m T Figure 4 A boy throws a ball at a target. At the instant when the ball leaves the boy’s hand at the point A, the ball is 2 m above horizontal ground and is moving with speed U at an angle alpha above the horizontal. In the subsequent motion, the highest point reached by the ball is 3 m above the ground. The target is modelled as being the point T, as shown in Figure 4. The ball is modelled as a particle moving freely under gravity. Using the model, g (a) show that U = alpha sin (2)
27. June 2018 · Paper 3 · Q10(b) · 9 marks
The point T is at a horizontal distance of 20 m from A and is at a height of 0.75 m above the ground. The ball reaches T without hitting the ground. (b) Find the size of the angle alpha (9)
28. June 2018 · Paper 3 · Q10(c) · 1 marks
(c) State one limitation of the model that could affect your answer to part (b). (1)
29. June 2018 · Paper 3 · Q10(d) · 3 marks
(d) Find the time taken for the ball to travel from A to T. (3)

Mark schemes

Each mark scheme shows the whole question; the parts on this topic are the ones listed above.

June 2025 · Paper 3 (Mechanics) · Q5
Mark scheme June 2025 Paper 3 (Mechanics) Q5(b)
June 2024 · Paper 3 (Mechanics) · Q5
Mark scheme June 2024 Paper 3 (Mechanics) Q5(e)
June 2023 · Paper 3 (Mechanics) · Q5
Mark scheme June 2023 Paper 3 (Mechanics) Q5(d)
June 2022 · Paper 3 (Mechanics) · Q5
Mark scheme June 2022 Paper 3 (Mechanics) Q5(d)
Oct 2021 · Paper 3 (Mechanics) · Q4
Mark scheme Oct 2021 Paper 3 (Mechanics) Q4(c)
Oct 2020 · Paper 3 (Mechanics) · Q5
Mark scheme Oct 2020 Paper 3 (Mechanics) Q5(d)
June 2019 · Paper 3 (Mechanics) · Q5
Mark scheme June 2019 Paper 3 (Mechanics) Q5(c)
June 2018 · Paper 3 · Q10
Mark scheme June 2018 Paper 3 Q10(d)