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A carrom board [4 ft. xx4 ft] has the qu...

A carrom board [`4 ft. xx4 ft`] 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 displacement of the queen from the centre to the frond edge?

Text Solution

Verified by Experts

The correct Answer is:
(a)`2/3sqrt(10)` (b)`4/3sqrt(10)` (c)`2sqrt(2)` ft
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`
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