Question

A striker is shot from a square carrom board from a point $A$ exactly at the midpoint of one of the walls with a speed of $2$ m/sec at an angle of ${45}^o$ with the x-axis as shown. The collisions of the striker with the walls of the fixed carrom are perfectly elastic. The coefficient of kinetic friction between the striker and the board is $0.2$. The coordinate of the striker when it stops (taking point $O$ to be the origin) is:

• A. $\frac{1}{2\sqrt{2}},\frac{1}{\sqrt{2}}$
• B. $0,\frac{1}{2\sqrt{2}}$
• C. $\frac{1}{2\sqrt{2}},0$
• D. $\frac{1}{\sqrt{2}},\frac{1}{2\sqrt{2}}$

Answer 1

The correct option is A $\frac{1}{2\sqrt{2}},\frac{1}{\sqrt{2}}$

the distance '$vc$' strikes transverse

$\sqrt{{\left(\frac{1}{2\sqrt{2}}\right)}^2+{\left(\frac{1}{2\sqrt{2}}\right)}^2}=\frac{1}{2}=0.5m=vc$

the KE goes into the heat emitted

$\frac{1}{2}{mv}^2=umgs$

total distance travelled by strikes

$\frac{v^2}{2ug}$

$=\frac{4}{2\times 0.2\times 10}=1m=vc$

the mid-point of topside coordinates of that point

$(\frac{1}{2\sqrt{2}},\frac{1}{\sqrt{2}})$