Find the velocity vector of stricker after 1021
collisions with the edges of smooth surfaced
carom board shown in the diagram. Assume all
collision are elastic and stricker collides with
every adjacent side in successive
Answers
Thus the coordinates of the sticker are ( 1 / 2√2 , 1/√2)
Explanation:
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 2 ms-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)
Solution:
Retardation, a = μmg / m = μg
= 0.2 × 10 = 2 m/s^2
Total distance travelled before coming to rest.
d = u^2 / 2a = (2)^2 / 2×2 = 1 m
x = 2 √L / 2 = L √2 = 1 / 2
Therefore striker will stop after travelling a distance 2x, as shown in figure.
Co-ordinates of point P are, (L2,L)
( 1 / 2√2 , 1/√2)
Thus the coordinates of the sticker are ( 1 / 2√2 , 1/√2)