Projectiles — AS & A Level Further Mathematics (9231) questions by topic

Projectile motion under gravity dominates this topic: finding the angle of projection when a particle passes a given point, determining where a particle strikes a vertical wall a fixed distance away, and expressing conditions for a particle to strike an inclined plane while moving horizontally.

Find, show, determine, express and derive lead the command words across 18 questions from 2023 to 2025 papers, worth from 5 to 11 marks, where resolving horizontal and vertical motion separately before combining them is the standard route. With no examiner-report extracts recorded here, checking each trajectory equation with instant marking is the way to catch a mixed-up horizontal and vertical component before it propagates through the rest of a multi-part projectile question.

May–June 2025, Paper 31

Question 2 · 6 marks

A particle P is projected with speed 24 m s^-1 at an angle theta degrees above the horizontal from a point O on a horizontal plane, and moves freely under gravity. At a horizontal…

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May–June 2025, Paper 32

Question 2 · 6 marks

A particle P is projected with speed 24 m s^-1 at an angle theta degrees above the horizontal from a point O on a horizontal plane, and moves freely under gravity. At a horizontal…

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May–June 2025, Paper 33

Question 7 · 11 marks

A particle P is projected from a point O with speed U at an angle 45 degrees above the horizontal and moves freely under gravity. State the vertical and horizontal components of…

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May–June 2025, Paper 34

Question 3 · 7 marks

A particle P is projected with speed u at an angle alpha above the horizontal from a point O on a horizontal plane and moves freely under gravity. The horizontal and vertical…

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May–June 2024, Paper 31

Question 3 · 5 marks

At time t = 0 seconds, a particle P is projected with speed u m s^-1 at an angle 60 degrees above the horizontal from a point O. In the subsequent motion P moves freely under…

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May–June 2024, Paper 32

Question 3 · 5 marks

At time t = 0 seconds, a particle P is projected with speed u m s^-1 at an angle 60 degrees above the horizontal from a point O. In the subsequent motion P moves freely under…

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May–June 2024, Paper 33

Question 6 · 8 marks

A particle P is projected with speed u m s^-1 at an angle theta above the horizontal from a point O and moves freely under gravity. After 5 seconds the speed of P is (3/4)u. Show…

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October–November 2024, Paper 31

Question 1 · 5 marks

A particle P is projected with speed u m s^-1 at an angle tan^-1(2) above the horizontal from a point O on a horizontal plane and moves freely under gravity. When P has travelled…

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Question 7 · 10 marks

A particle P is projected with speed u at an angle tan^-1(4/3) above the horizontal from a point O on a horizontal plane and moves freely under gravity. When P is moving…

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October–November 2024, Paper 32

Question 5 · 8 marks

A particle P is projected from a point O on horizontal ground with speed u at an angle theta above the horizontal, where tan theta = 1/3. The particle P moves freely under gravity…

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October–November 2024, Paper 33

Question 1 · 5 marks

A particle P is projected with speed u m s^-1 at an angle tan^-1 2 above the horizontal from a point O on a horizontal plane and moves freely under gravity. When P has travelled a…

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Question 7 · 10 marks

A particle P is projected with speed u at an angle tan^-1(4/3) above the horizontal from a point O on a horizontal plane and moves freely under gravity. When P is moving…

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May–June 2023, Paper 31

Question 7 · 9 marks

At time t s, a particle P is projected with speed 40 m s^-1 at an angle theta above the horizontal from a point O on a horizontal plane and moves freely under gravity. The…

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May–June 2023, Paper 32

Question 7 · 9 marks

At time t s, a particle P is projected with speed 40 m s^-1 at an angle theta above the horizontal from a point O on a horizontal plane and moves freely under gravity. The…

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May–June 2023, Paper 33

Question 7 · 9 marks

The points O and P are on a horizontal plane, a distance 8 m apart. A ball is thrown from O with speed u m s^-1 at an angle theta above the horizontal, where tan theta = 4/3. At…

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October–November 2023, Paper 31

Question 5 · 9 marks

A particle P is projected with speed u m s^-1 at an angle theta above the horizontal from a point O on a horizontal plane and moves freely under gravity. During its flight P…

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October–November 2023, Paper 32

Question 6 · 9 marks

A particle P is projected with speed u at an angle alpha above the horizontal from a point O on a horizontal plane and moves freely under gravity. The horizontal and vertical…

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October–November 2023, Paper 33

Question 5 · 9 marks

A particle P is projected with speed u m s^-1 at an angle theta above the horizontal from a point O on a horizontal plane and moves freely under gravity. During its flight P…

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