Motion of a projectile: past paper questions

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• Question 7May/June 2026, paper 31Structured6 marks

  The points $O$ and $A$ lie on a horizontal plane $10\text{ m}$ apart. The point $A$ lies at the foot of another plane which is inclined at an angle of $\alpha$ above the horizontal such that $\tan \alpha =\frac{4}{3}$.

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• Question 7Oct/Nov 2025, paper 31Structured12 marks

  A particle $P$ is projected from a point $O$ on a horizontal plane and moves freely under gravity. The initial velocity of $P$ is $25{\mathrm{m}\mathrm{s}}^{-1}$ at an angle $\theta$ above the horizontal, where $\tan \theta =\frac{4}{3}$.

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• Question 1Oct/Nov 2024, paper 31Structured5 marks

  A particle $P$ is projected with speed $u\mathrm{m}{\mathrm{s}}^{-1}$ at an angle ${\tan }^{-1}2$ above the horizontal from a point $O$ on a horizontal plane and moves freely under gravity.

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• Question 5Oct/Nov 2023, paper 31Structured9 marks

  A particle $P$ is projected with speed $u{\text{ ms}}^{-1}$ at an angle $\theta$ above the horizontal from a point $O$ on a horizontal plane and moves freely under gravity.

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• Question 4Oct/Nov 2025, paper 32Structured7 marks

  A particle $Q$ is initially positioned at a distance $d$ vertically above a particle $P$. Particle $P$ is projected with speed $U$ at an angle $\alpha$ above the horizontal. At the same time, $Q$ is projected at an angle $\beta$ below the horizontal.

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• Question 7Oct/Nov 2024, paper 31Structured10 marks

  A particle $P$ is projected with speed $u$ at an angle ${\tan }^{-1}\left(\frac{4}{3}\right)$ above the horizontal from a point $O$ on a horizontal plane and moves freely under gravity. When $P$ is moving horizontally, it strikes a smooth inclined plane at the point $A$.

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• Question 7May/June 2026, paper 33Structured8 marks

  At time $t=0\mathrm{s}$, a particle $P$ is projected from a point $O$ on horizontal ground. The initial velocity of $P$ is $25{\mathrm{m}\mathrm{s}}^{-1}$ at an angle $\alpha$ above the horizontal, where $\sin \alpha =\frac{4}{5}$.

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• Question 6Oct/Nov 2025, paper 32Structured8 marksHas a diagram

  A fixed smooth sphere with radius $a$ and centre $O$ rests on horizontal ground. A particle is projected horizontally from the highest point, $A$, of the sphere with speed $u$. The particle begins to move in a vertical circle along the surface of the sphere.

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• Question 5Oct/Nov 2024, paper 32Structured8 marks

  A particle $P$ is projected from a point $O$ on horizontal ground with speed $u$ at an angle $\theta$ above the horizontal, where $\tan \theta =\frac{1}{3}$.

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• Question 7May/June 2023, paper 31Structured9 marks

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

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• Question 7Oct/Nov 2025, paper 33Structured12 marks

  A particle $P$ is projected from a point $O$ on a horizontal plane and moves freely under gravity. The initial velocity of $P$ is $25\mathrm{m}{\mathrm{s}}^{-1}$ at an angle $\theta$ above the horizontal, where $\tan \theta =\frac{4}{3}$.

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• Question 1Oct/Nov 2024, paper 33Structured5 marks

  A particle $P$ is projected with speed $u\text{m}{\text{s}}^{-1}$ at an angle ${\tan }^{-1}2$ above the horizontal from a point $O$ on a horizontal plane and moves freely under gravity.

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• Question 2May/June 2025, paper 31Structured6 marks

  A particle $P$ is projected with speed $24\text{ m}{\text{s}}^{-1}$ at an angle ${\theta }^{\circ }$ above the horizontal from a point $O$ on a horizontal plane, and moves freely under gravity.

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• Question 7May/June 2023, paper 33Structured9 marks

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

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• Question 7May/June 2025, paper 31Structured10 marksHas a diagram

  A fixed hollow sphere has radius $a$ and centre $O$. The points $A$, $B$ and $C$ lie on the inner surface of the sphere with $OA$ and $BC$ horizontal.

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• Question 3May/June 2024, paper 31Structured5 marks

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

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• Question 7May/June 2024, paper 31Structured9 marks

  A smooth sphere with centre $O$ and of radius $a$ is fixed to a horizontal plane. A particle $P$ of mass $m$ is projected horizontally from the highest point of the sphere with speed $u$, so that it begins to move along the surface of the sphere.

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• Question 3May/June 2024, paper 32Structured5 marks

  At time $t=0$ seconds, a particle $P$ is projected with speed $u{\text{ ms}}^{-1}$ at an angle ${60}^{\circ }$ above the horizontal from a point $O$. In the subsequent motion $P$ moves freely under gravity.

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• Question 5May/June 2025, paper 33Structured8 marksHas a diagram

  A hollow cylinder of radius $r$ is fixed with its axis horizontal. Points $A$, $B$ and $O$ are in the same vertical plane perpendicular to the axis of the cylinder, with $A$ and $B$ on the smooth inner surface and $O$ on the axis.

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• Question 7May/June 2025, paper 33Structured11 marks

  A particle $P$ is projected from a point $O$ with speed $U$ at an angle ${45}^{\circ }$ above the horizontal and moves freely under gravity. State the vertical and horizontal components of velocity at time $t$.

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• Question 6May/June 2024, paper 33Structured8 marks

  A particle $P$ is projected with speed $u{\text{ ms}}^{-1}$ at an angle $\theta$ above the horizontal from a point $O$ and moves freely under gravity. After 5 seconds the speed of $P$ is $\frac{3}{4}u$. Show that $\frac{7}{16}{u}^2-100u\sin \theta +2500=0$.

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