Two particles A and B move with constant velocities $\overrightarrow{v}_1$ and $\overrightarrow{v}_2$ . At the initial moment their position vectors are $\overrightarrow{r_1}$ and $\overrightarrow{r}_2$ respectively. The condition for particles A and B to collide is:
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Question

Two particles A and B move with constant velocities $\overrightarrow{v}_1$ and $\overrightarrow{v}_2$ . At the initial moment their position vectors are $\overrightarrow{r_1}$ and $\overrightarrow{r}_2$ respectively. The condition for particles A and B to collide is:

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G1 Physics · Accepted Answer

Step 1: At collision, r₁+v₁t = r₂+v₂t. Step 2: Therefore r₁-r₂ = (v₂-v₁)t. Step 3: Since collision occurs for a positive time, r₁-r₂ and v₂-v₁ must be parallel and in the same direction. Their unit vectors must therefore be equal. Final answer: A.