A carrom board `4ftxx4ft` square has the queen at the centre. The queen hit by the striker moves to the front edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen (a). from the centre to the front edge (b). from the front edge to the hole and (c). from the centre to the hole.

Explanation

Compare triangle PAQ and ONP
`tan theta=(2-x)/(4)=(x)/(2)rArr4-2x=4x`
`therefore=(4)/(6)=(2)/(3)` ft.
In `DeltaOPN OP=sqrt(ON^(2)+PN^(2))=sqrt(((2)/(3))^(2)+(2)^(2))=sqrt((40)/(9))=(2)/(3)sqrt(10)ft.