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 te hole behind the striking line. Find the magnitude of displacement of the queen a. from the centre to the front edge b. from teh front edge to teh hole and c. from the centre to teh hole.

Answer

(a)`2/3sqrt(10)` (b)`4/3sqrt(10)` (c)`2sqrt(2)` ft

Explanation

In `/_\\\\ABC, tan theta = x/2`
and `in /_\\\\ DCE, tan theta = (2-x)/4, tan theta= x/2=(2-x)/4
rarr 2(2-x)=4x
rarr 4-2x=4x
rarr 6x=4
rarr x=2/3 ft
(a). In /_\\\\ ABC
AC= sqrt(AB^2+BC^2)
(sqrt(2/3)^2+2^2)
sqrt(4/9+4)=sqrt(40/9)
=2/3 sqrt(10) ft
(b). In /_\\\\CDE, DE= 2-2/3=(6-2)/3=4/3 ft
sin CD= 4ft
` there CE
`=sqrt(CD^2+DE^2)
=(sqrt4^2+(4/3)^2)/=4/3sqrt(10) ft
(c). In /_\\\\ AGE
AE = sqrt(AG^2+GE^2)
sqrt(2^2+2^2)
=sqrt(8)=2sqrt(2) ft`