Momentum: past paper questions

Where the questions come from

• Question 4May/June 2026, paper 31Structured8 marks

  A particle $P$ is moving on a fixed smooth horizontal surface with speed $u$. The particle collides with a fixed smooth vertical barrier. Immediately before the collision, the direction of motion of $P$ makes an angle $\alpha$ with the barrier, where $\tan \alpha =\frac{12}{5}$.

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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 6Oct/Nov 2025, paper 31Structured8 marksHas a diagram

  A particle $P$ of mass $m$ is attached to one end of a light inextensible string of length $a$. The other end of the string is attached to a fixed point $O$. Initially $P$ is held with the string taut and making an angle of ${60}^{\circ }$ with the upward vertical through $O$.

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• Question 3Oct/Nov 2024, paper 32Structured7 marksHas a diagram

  The diagram shows two identical smooth uniform spheres $A$ and $B$ of equal radii and each of mass $m$. The two spheres are moving on a smooth horizontal surface when they collide with speeds $2u$ and $3u$ respectively.

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• Question 5May/June 2026, paper 33Structured6 marksHas a diagram

  Two uniform smooth spheres $A$ and $B$ of equal radii and equal masses $m$ are moving with speeds $u_A$ and $u_B$ respectively on a smooth horizontal surface when they collide.

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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 2May/June 2023, paper 31Structured5 marksHas a diagram

  A particle $P$ of mass $m$ is moving with speed $u$ on a fixed smooth horizontal surface. It collides at an angle $\alpha$ with a fixed smooth vertical barrier. After the collision, $P$ moves at an angle $\theta$ with the barrier, where $\tan \theta =\frac{1}{2}$ (see diagram).

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• Question 6May/June 2026, paper 33Structured11 marks

  A smooth plane is inclined at an angle $\theta$ to the horizontal, where $\sin \theta =\frac{4}{5}$. One end of a light elastic spring, with natural length $10a$ and modulus of elasticity $1.6mg$, is attached to a fixed point $O$ on the plane.

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• Question 5Oct/Nov 2025, paper 32Structured9 marksHas a diagram

  Two uniform smooth spheres, $A$ and $B$, of equal radii are on a horizontal surface. They have masses of $m$ and $km$ respectively. Sphere $A$ is moving with speed $u$ at an angle $\alpha$ with the line of centres when it collides with sphere $B$ which is stationary.

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• Question 2May/June 2023, paper 32Structured5 marksHas a diagram

  A particle $P$ of mass $m$ is moving with speed $u$ on a fixed smooth horizontal surface. It collides at an angle $\alpha$ with a fixed smooth vertical barrier. After the collision, $P$ moves at an angle $\theta$ with the barrier, where $\tan \theta =\frac{1}{2}$ (see diagram).

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• Question 4May/June 2023, paper 33Structured8 marksHas a diagram

  Two identical smooth uniform spheres $A$ and $B$ each have mass $m$. The two spheres are moving on a smooth horizontal surface when they collide with speeds $u$ and $2u$ respectively.

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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 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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