Show that the motion of one projectile as seen from another projectile will always be a straight line motion.

Explanation

Let the two projectiles be thrown from (O) in the ` X-Y` plane with velcityes ` u_(1)` and `u_(2)` making angles ` theta_(1) and theta_(2)` respectively with x-axis. After time (t) let one projectile reaches at (A) `(x_(1)`,` y_(1))` and another projectile reaches at ` B (x_(2), y_(2)). Fig. 2 (d).32. Then
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` x_(1) =u_(2) cos theta_(1) t and y_(1) =u_(1) sin theta _(1) t- 1/2 gt^(2)`
Also ` x_(2) =u_(2) cos sin theta_(2) t`
and ` y_(2) =u_(2) sin theta -1/2 gt^(2)`
:. ` x_(2) -x_(1) =u_(2) sin sin theta_(2) u_(1) cos theta_(1))t`
`y2-y_(1) = (u^(2) sin _(2) -u_(1) sin theta_(1))t`
or ` (y_(2)-y_(1)/(x_(2)-x_(2)= (u_(2) sin theta_(2) -u_(1) sin theta_(1))/(u_(2) cos theta_(2)-u_(1) cos theta_(1))`
`= k (a constant)`
Let ` x, y` be coordingate of point (B) w.r.t. Point
`A then x_(2) -x_(1) =x and y_(2) -y_(1) =y`
:. y/x =(y_(2) -y_(1))/(x_(2)-x_(2)) =k or y=kx`
which is epuation of a straight line. Hence the motion of one projectile as seen from anothr projectile is a straigght line motion.