Two-particles-1-and-2-move-with-constant-velocities-v-1-and-v-2-At-the-initial-moment-their-position-vectors-are-equal-to-r-1-and-r-2-How-must-these-four-vectors-be-interr

Question Number 16294 by Tinkutara last updated on 20/Jun/17

Two particles, 1 and 2, move with

constant velocities \vec{v_{1}} and \vec{v_{2}} . At the

initial moment, their position vectors

are equal to \vec{r_{1}} and \vec{r_{2}} . How must these

four vectors be interrelated for the

particle to collide ?

Commented by prakash jain last updated on 21/Jun/17

For the particle to collide they

should meet at some time t .

r_{1} + v_{1} t = r_{2} + v_{2} t

\Rightarrow (r_{1} - r_{2}) = (v_{2} - v_{1}) t

t is a scaler so it implies that

r_{1} - r_{2} is parallel to v_{2} - v_{1} .

Answered by ajfour last updated on 20/Jun/17

({\vec{r}}_{2} - {\vec{r}}_{1}) \times ({\vec{v}}_{1} - {\vec{v}}_{2}) = 0, i t h i n k .

t h a t i s t h e i r r e l a t i v e v e l o c i t y

m u s t n o t b e a l o n g a n y o t h e r l i n e

b u t t h a t o f ({\vec{r}}_{2} - {\vec{r}}_{1}) .

Commented by Tinkutara last updated on 20/Jun/17

But answer is \frac{{\vec{v}}_{1} - \vec{v_{2}}}{∣ \vec{v_{1}} - \vec{v_{2}} ∣} = \frac{{\vec{r}}_{2} - \vec{r_{1}}}{∣ \vec{r_{2}} - \vec{r_{1}} ∣}

Commented by Tinkutara last updated on 20/Jun/17

OK . I will recheck .

Commented by Tinkutara last updated on 22/Jun/17

Thanks Sir!

Commented by prakash jain last updated on 21/Jun/17

Hi ajfour,

i think {book}^{'} s answer is correct .

Cross product could be 0 even

if t < 0 (see comment in question) .

{book}^{'} s answer implies t > 0 .