Two particles are projected from the same point, with the same speed, in the same vertical plane, at different angles with the horizontal.A frame of references is fixed to one particle.The position vector of the other particle as observed from this frame is `vecr`Which of the following statements are corrects?

Options

A. direction of `vecr` does not change
B. `vecr` changes in magnitudes and direction with time
C. The magnitude of `vecr` increases linearly with time
D. The direction of `vecr` changes with time, its magnitude may or may not change, depending on the angles of projection

Answer

A, C

Explanation

Let `u`= the speed of projection, `theta_(1)` and `theta_(2)`= the angles of projection. Let `vecr_(1)` and `vecr_(2)` be the position vectors of the two particles in a ground frame. `vecr_(1)`
`=(u cos theta_(1)),thati+[(usintheta_(1))t-1/2"gt"^(2)]hatj`
`vecr_(2)=(u cos theta_(2))t hati+[(usintheta_(2))t-1/2"gt"^(2)]hatj`
The position vector of one particle with respect to another is `vecr=vecr_(1)-vecr_(2)=[u (cos theta_(1)-cos theta_(2))t]hati+[u(sin theta_(1)-sin theta_(2)t]hatj=at hati+bt hatj=[ahati+bhatj]t`,
where `a` and `b` are constants.