Question

$\huge{\boxed{Question}}$


➡️Two particles, 1 and 2 moves with constant velocities v₁ and v₂ . At the initial moment their radius vectors are equal to r₁ and r₂ . How must these four vectors be interrelated for the particles to collide.



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Answer 1

Answer:

$\frac{v_1 - v_2}{|v_1 - v_2|} = \frac{r_1 - r_2}{|r_1 - r_2|}$

Explanation:

Given :

Two particles, 1 and 2 moves with constant velocities v₁ and v₂ .

At the initial moment their radius vectors are equal to r₁ and r₂ .

How must these four vectors be interrelated for the particles to collide.

Solution :

Let the particle 1 be A & 2 be B

For the particles to collide,

They must be directed towards each other,.

⇒ They must have the ratio of relative velocity & relative position equal

Direction of Velocity of Particle A with respect to B

⇒ $v_A - v_B$

Position of Particle A with respect to B

⇒ $r_A - r_B$

Particle A will collide with B, when velocity A with respect to B is directed towards B

⇒ $\frac{v_A - v_B}{|v_A - v_B|} = \frac{r_A - r_B}{|r_A - r_B|}$

Answer 2

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