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Edexcel A-Level Mathematics A2 M2.4.3 Successive Impacts of Up to Three Questions

Practise successive impacts involving particles and smooth walls, linking rebound speeds, timing, energy changes and conditions for another collision.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • use wall restitution to update rebound speed before deciding whether a second collision occurs
  • find ranges for e or f from inequalities comparing particle speeds after a wall rebound

Edexcel A-Level Mathematics A2 M2.4.3 Successive Impacts of Up to Three Questions question 1

[Maximum number: 3]

Particle P has mass 4 m and particle Q has mass 2 m.

The particles are moving in opposite directions along the same straight line on a smooth horizontal surface.

Particle P collides directly with particle Q.
Immediately before the collision, the speed of P is 2 u and the speed of Q is 3 u.
Immediately after the collision, the speed of P is x and the speed of Q is y.
The direction of motion of each particle is reversed as a result of the collision.
The total kinetic energy of P and Q after the collision is half of the total kinetic energy of P and Q before the collision.

find the range of possible values of f.

Given that f=14f=\frac{1}{4}

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