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
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…
Answer this question and get it marked →May–June 2025, Paper 32
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…
Answer this question and get it marked →May–June 2025, Paper 33
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…
Answer this question and get it marked →May–June 2025, Paper 34
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…
Answer this question and get it marked →May–June 2024, Paper 31
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…
Answer this question and get it marked →May–June 2024, Paper 32
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…
Answer this question and get it marked →May–June 2024, Paper 33
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…
Answer this question and get it marked →October–November 2024, Paper 31
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…
Answer this question and get it marked →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…
Answer this question and get it marked →October–November 2024, Paper 32
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…
Answer this question and get it marked →October–November 2024, Paper 33
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…
Answer this question and get it marked →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…
Answer this question and get it marked →May–June 2023, Paper 31
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…
Answer this question and get it marked →May–June 2023, Paper 32
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…
Answer this question and get it marked →May–June 2023, Paper 33
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…
Answer this question and get it marked →October–November 2023, Paper 31
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…
Answer this question and get it marked →October–November 2023, Paper 32
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…
Answer this question and get it marked →October–November 2023, Paper 33
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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