A striker is shot from a square carom board from a point A exactly at midpoint of one of the walls with a speed of `2ms^-1` at an angle of `45^@` with the x-axis as shown in the figure. The collisions of the striker with the walls of the fixed carom are perfectly elastic. The coefficient of kinetic friction between the striker and board is `0.2`. The coordinate of the striker when it stops (taking point O to be origin) is (in SI units)

Options

A. (a) `(1)/(2sqrt2)`, `(1)/(sqrt2)`
B. (b) `0`, `(1)/(2sqrt2)`
C. (c) `(1)/(2sqrt2)`, `0`
D. (d) `(1)/(sqrt2)`, `(1)/(2sqrt2)`

Answer

A

Explanation

Retardation, `a=(mumg)/(m)=mug`

`=0.2xx10=2m//s^2`
Total distance travelled before coming to rest,
`d=(u^2)/(2a)=((2)^2)/(2xx2)=1m`
`x=sqrt2L/2=L/sqrt2=1/2`
`=0.5m`
Therefore striker will stop after travelling a distance `2x`, as shown in figure.

Co-ordinates of point P are, `(L/2, L)`
or `((1)/(2sqrt2), (1)/(sqrt2))`