The point $$\(A\)$$ lies on a smooth horizontal floor between two fixed smooth parallel vertical walls $$\(W X\)$$ and $$\(Y Z\)$$, as shown in the plan view in Figure 1. The distance between $$\(W X\)$$ and $$\(Y Z\)$$ is $$\(3 d\)$$. The distance of $$\(A\)$$ from $$\(Y Z\)$$ is $$\(d\)$$. A particle is projected from $$\(A\)$$ along the floor with speed $$\(u\)$$ towards $$\(Y Z\)$$ in a direction perpendicular to $$\(Y Z\)$$. The coefficient of restitution between the particle and each wall is $$\(\frac{2}{3}\)$$ The time taken for the particle to move from $$\(A\)$$, bounce off each wall once and return to $$\(A\)$$ for the first time is $$\(T_{1}\)$$ (a) Find $$\(T_{1}\)$$ in terms of $$\(d\)$$ and $$\(u\)$$. (5) The ball returns to $$\(A\)$$ for the first time after bouncing off each wall once. The further time taken for the particle to move from $$\(A\)$$, bounce off each wall once and return to $$\(A\)$$ for the second time is $$\(T_{2}\)$$ (b) Find $$\(T_{2}\)$$ in terms of $$\(d\)$$ and $$\(u\)$$. (1)

Answer:

Knowledge points:

Solution: