Two particles are projected simultaneously in the same vertical plane from the same point, with different speeds `u_(1)` and `u_(2)`, making angles `theta_(1)` and `theta_(2)` respectively with the horizontal, such that `u_(1) cos theta_(1) = u_(2) cos theta_(2)`. The path followed by one, as seen by the other (as long as both are in flight), is

Options

A. a vertical line
B. a parabola
C. a hyperbola
D. a straight line making a constant angle `(ne 90^(@))` with horizontal

Answer

D

Explanation

Let `vecu_(1)` and `u_(2)` be the initial velocities of the two particles and `theta_(1)` and `theta_(2)` be their angles of projection with the horizontal.
The velocities of the two particles after tiem t are,
`vecv_(1) = (u_(1) cos theta_(1)) hati + (u_(1) sin theta_(1) - "gt")hatj`
and `vecv_(2) = (u_(2) cos theta_(2)) hati + (u_(2) sin theta_(2) - "gt") hatj`
`vecv_(12) = vecv_(1) - vecv_(2) = (u_(1) cos theta_(1) - u_(2) cos theta_(2)) hati + (u_(1) sin theta_(1) - u_(2) sin theta_(2)) hatj` Which is a constant. So the path followed by one,as seen by the other is straight line, making a constant angle with the horizontal.