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 hole.

Step-by-step solution

Let the carrom board be represented in a coordinate system with its corners at (0,0) , (4,0) , (4,4) , and (0,4) . The initial position of the queen is at the centre of the board, which has coordinates (2,2) . The final position of the queen is the hole behind the striking line. Without loss of generality, let this hole be at the origin (0,0) . Although the queen travels to the front edge and rebounds, displacement is defined as the shortest straight-line distance between the initial and final positions, independen