A2 June 2019 Q2

EdexcelCurrent spec11 marksCollisions: 1 Sphere Oblique

2.

Figure 2: plan view of perpendicular walls AB and BC meeting at B; the ball approaches AB at 6 m/s at angle α to AB, leaves AB at angle β to AB, and then hits BC
Figure 2

Figure 2 represents the plan view of part of a horizontal floor, where \(AB\) and \(BC\) are fixed vertical walls with \(AB\) perpendicular to \(BC\).

A small ball is projected along the floor towards \(AB\) with speed \(6\ \text{m s}^{-1}\) on a path that makes an angle \(\alpha\) with \(AB\), where \(\tan\alpha = \dfrac{4}{3}\). The ball hits \(AB\) and then hits \(BC\).

Immediately after hitting \(AB\), the ball is moving at an angle \(\beta\) to \(AB\), where \(\tan\beta = \dfrac{1}{3}\)

The coefficient of restitution between the ball and \(AB\) is \(e\).

The coefficient of restitution between the ball and \(BC\) is \(\dfrac{1}{2}\)

By modelling the ball as a particle and the floor and walls as being smooth,

(a) show that the value of \(e = \dfrac{1}{4}\) (5)
(b) find the speed of the ball immediately after it hits \(BC\). (4)
(c) Suggest two ways in which the model could be refined to make it more realistic. (2)
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