The figure shows a square carrom board without any pockets. A coin is pushed from the corner, which is the origin, with a velocity overset arrow v=(.2 hati+3 hatj.) . Assume gravity and friction to be absent. The coin collides with edges of the carrom board elastically. What is the velocity vector of coin after the 3 textrd collision ?

Question

The figure shows a square carrom board without any pockets. A coin is pushed from the corner, which is the origin, with a velocity overset arrow v=(.2 hati+3 hatj.) . Assume gravity and friction to be absent. The coin collides with edges of the carrom board elastically. What is the velocity vector of coin after the 3 textrd collision ? <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-vnyj07jglebm0sh5.jpg" /> (A) 2 hati+3 hatj (B) 2 hati-3 hatj (C) -2 hati+3 hatj (D) -2 hati-3 hatj

Tardigrade Admin · Accepted Answer

After each collision normal components of velocity gets reversed.

∴

after

1^{st}

collision, velocity of coin,

v \to_{1} = 2 \hat{i} - 3 \hat{j}

after

2^{st}

collision, velocity of coin,

v \to_{2} = - 2 \hat{i} - 3 \hat{j}

after

3^{rd}

collision, velocity of coin,

v \to_{3} = - 2 \hat{i} + 3 \hat{j}

$2 \hat{i} + 3 \hat{j}$

$2 \hat{i} - 3 \hat{j}$

$- 2 \hat{i} + 3 \hat{j}$

$- 2 \hat{i} - 3 \hat{j}$

2i^+3j^​

2i^−3j^​

−2i^+3j^​

−2i^−3j^​

After each collision normal components of velocity gets reversed. ∴ after 1st collision, velocity of coin, v→1​=2i^−3j^​ after 2st collision, velocity of coin, v→2​=−2i^−3j^​ after 3rd collision, velocity of coin, v→3​=−2i^+3j^​

$2 \hat{i} + 3 \hat{j}$

$2 \hat{i} - 3 \hat{j}$

$- 2 \hat{i} + 3 \hat{j}$

$- 2 \hat{i} - 3 \hat{j}$