Question

Two point masses 1 and 2 move with uniform velocities `vec(v)_(1)` and `vec(v)_(2)`, respectively. Their initial position vectors are `vec(r )_(1)` and `vec(r )_(2)`, respectively. Which of the following should be satisfied for the collision of the point masses?
A. `(vec(r )_(1)-vec(r )_(2))/(|vec(r )_(2)-vec(r )_(1)|)=(vec(v)_(2)-vec(v)_(1))/(|vec(v)_(2)-vec(v)_(1)|)`
B. `(vec(r )_(2)-vec(r )_(1))/(|vec(r )_(2)-vec(r )_(1)|)=(vec(v)_(2)-vec(v)_(1))/(|vec(v)_(2)-vec(v)_(1)|)`
C. `(vec(r)_(2)-vec(r )_(1))/(|vec(r )_(2)+vec(r )_(1)|)=(vec(v)_(2)-vec(v)_(1))/(|vec(v)_(2)+vec(v)_(1)|)`
D. `(vec(r)_(2)-vec(r )_(1))/(|vec(r )_(2)+vec(r )_(1)|)=(vec(v)_(2)-vec(v)_(1))/(|vec(v)_(2)+vec(v)_(1)|)`

Answer 1

Correct Answer - B
For collision,

`vec(r )_(1)+vec(v)_(1)t=vec(r )_(2)+vec(v)_(2)t`
or `vec(r )_(1)-vec(r )_(2)=(vec(v)_(2)-vec(v)_(1))t`
Equating unit vectors, we get
`(vec(r )_(1)-vec(r )_(2))/(|vec(r )_(2)-vec(r )_(1)|)=(vec(v)_(2)-vec(v)_(1))/(|vec(v)_(2)-vec(v)_(1)|)`