A carom board (4 ft x 4 ft square) has the queen at the center. 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 center to the front edge, (b) from the front edge to the hole and (c) from the center to the hole.

Question

Philoid · Accepted Answer

Let O is the center of the carom board. P is the point on the front edge where queen strikes. PA is the rebound path.

Like the reflection of the light, OP and PA will make equal angle θ with the normal at P. From the figure PQ=OQ tan θ =2tan θ and DP=DA tanθ =4 tanθ,

DQ =DP+PQ = 2 tanθ + 4 tanθ =6 tan θ = 2, tan θ =1/3

Now Magnitude of displacement of the queen from.

(a) the center to the front edge OP = =

(b)the front edge to hole =PA = = ==(4√10)/3 ft

(c) the center to the hole OA = =√8 =2√2 ft