Two particles A and B, move with constant velocities v₁ and v₂. At the initial moment their position vectors are r₁ and r₂ respectively. The condition for particles A and B for their collision is (a) r₁ × v₁ = r₂ × v₂ (b) r₁ - r₂ = v₁ - v₂ (c) (r₁ - r₂)/(|r₁ - r₂|) = (v₂ - v₁)/(|v₂ - v₁|) (d) r₁ · v₁ = r₂ · v₂

Answer: (c). Collision at time t: r₁ + v₁ t = r₂ + v₂ t r₁ - r₂ = ( v₂ - v₁)t with t > 0, so the two vectors point the same way. Equal unit vectors: ( r₁ - r₂)/(| r₁ - r₂|) = ( v₂ - v₁)/(| v₂ - v₁|) So the answer is (c).

Two particles A and B, move with constant velocities v₁ and v₂. At… | NEET 2015 (AIPMT)

Q9NEET 2015 · AIPMTMedium

Collisions

Two particles A and B, move with constant velocities $\vec{v}_1$ and $\vec{v}_2$ . At the initial moment their position vectors are $\vec{r}_1$ and $\vec{r}_2$ respectively. The condition for particles A and B for their collision is

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Answer: (c)

Collision at time $t$ : $\vec r_1 + \vec v_1 t = \vec r_2 + \vec v_2 t$
$\vec r_1 - \vec r_2 = (\vec v_2 - \vec v_1)t$ with $t > 0$ , so the two vectors point the same way.
Equal unit vectors: $\frac{\vec r_1 - \vec r_2}{|\vec r_1 - \vec r_2|} = \frac{\vec v_2 - \vec v_1}{|\vec v_2 - \vec v_1|}$
So the answer is (c).

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