A carrom board $[4 f t \times 4 ft square]$ has the queen at the centre. The queen hit by the striker moves to the front edge, rebounds and goes into the hole behind the striking line. Then find the magnitude of displacement of the queen

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From the centre of the front edge is

\frac{4}{3} \sqrt{10} ft

From the front edge to the hole is

\frac{4}{3} \sqrt{10} ft

From the centre to the front edge is

\frac{2}{3} \sqrt{10} ft

From centre to the hole is

2 \sqrt{2} ft

answer is A, B, C.

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Detailed Solution

$Δ BEC ≅ Δ DFC$ (by ASA property)

So, CF = EC (C.P.C.T)

And AE = EC (by reflection property)

AE = EC = CF $= 2/3$

$So, {AB}^{2} = {AE}^{2} + {BE}^{2}$

$= {(\frac{2}{3})}^{2} + {(2)}^{2}$

$= \frac{4}{9} + 4$

$= \frac{40}{9}$

$Displacement AB = \frac{2}{3} \sqrt{10} units$

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