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

Practise successive impacts involving particles and smooth walls, updating rebound speeds, comparing travel times, and deriving the coefficient ranges needed for another collision.

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

[Maximum number: 3]

Particle P has mass m and particle Q has mass 5 m.

The particles are moving in the same direction 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 6 u and the speed of Q is u.
Immediately after the collision, the speed of P is x and the speed of Q is y.
The direction of motion of P is reversed as a result of the collision.
The coefficient of restitution between P and Q is e.

find the complete range of possible values of f.

velocity of Q after collision with wall
$= \pm f y \quad\left(= \pm f \times \frac{7}{3} u\right)$

B1ft

Follow their y (in terms of u )

Second collision if $f y>x \frac{7}{3} f u>\frac{2}{3} u$
Correct inequality for their x, y
Dependent on the B1 and P moving
away from the wall

$\frac{2}{7}<f,, 1$
Correct only
Need both limits

[3]

(14)

All question bank results loaded

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