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Relative Velocity in 2D

Two particles...

Question

Two particles having position vectors $_{1} = 3^i + 5^j$ m and $_{2} = - 5^i + 3^j$ m are moving with velocities $_{1} = 4^i + 3^j$ m/s and $_{2} = - a^i + 4^j$ m/s. If they collide after $2$ seconds, the value of $a$ is:

A

- 2

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B

- 4

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C

- 6

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D

- 8

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Solution

The correct option is C $- 8$
For collision, their position vectors at $t = 2$ should be same. Hence
$3^i + 5^j + 2 (4^i + 3^j) = - 5^i + 3^j + 2 (- a^i + 4^j)$
$⟹ 11^i + 11^j = - (5 + 2 a)^i + 11^j$
$⟹ 5 + 2 a = - 11$
$⟹ a = - 8$

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