Two particles having position vectors and are moving with velocities m/s and m/s. If they collide after 2 sec, the value of 'a' is

Engineering

Physics

Collision

Question

Two particles having position vectors ${\vec{r}}_{1} = (3 \hat{i} + 5 \hat{j}) m$ and ${\vec{r}}_{2} = (- 5 \hat{i} - 3 \hat{j}) m$ are moving with velocities ${\vec{v}}_{1} = (4 \hat{i} + 3 \hat{j})$ m/s and ${\vec{v}}_{2} = (a \hat{i} + 7 \hat{j})$ m/s. If they collide after 2 sec, the value of 'a' is

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${\vec{r}}_{1} + {\vec{v}}_{1} t = {\vec{r}}_{2} + {\vec{v}}_{2} t$

$(3 \hat{i} + 5 \hat{j}) + (8 \hat{i} + 6 \hat{j}) = (- 5 \hat{i} - 3 \hat{j}) + (2 a \hat{i} + 14 \hat{j})$

11 = –5 + 2a
a = 8