A carrom board ( 4 ft 4 ft square) features the queen at its centre. The queen is struck by the striker, travels to the front edge, rebounds, and goes into the hole behind the striking line. Calculate the magnitude of displacement of the queen from the centre to the front edge.

Step-by-step solution

Let the carrom board be placed in the xy -plane with its corners at (0,0) , (4,0) , (4,4) , and (0,4) . The centre of the board where the queen is initially placed is at (2,2) . Let the front edge be the line y=4 and the hole behind the striking line be at the origin (0,0) . Let the queen strike the front edge at a point (x,4) . According to the law of reflection, the angle of incidence equals the angle of reflection. This implies that the ratio of the horizontal distances covered is equal to the ratio of the verti