Question

prove that the path of a projectile with respect to another projectile is a straight line

Answer 1

When u r sitting on a one prohectile(that means u r the 2 shadows of a particle obswerving shadows of another particle), u will see the the other shadow moving linearly with relative velocity on floor and with relative accelerated linear motion on the rear wall...
Hence it will still look like a projectile but, with different velocity, acceleration parameters


Now, if both the particles, the one on which u r sitting, and the other one that u r observing, are travelling with same vertical acceleration, then their relative acceleration will become zero.. so in that case the other particle wil b seen as travelling in a straight line.
it can also be explained as
The acceleration of both the projectiles is g.
So the relative acceleration between the projectiles is zero. That means their relative velocity is not changing. So even the direction is not changing changing(because relative acc. is zero).
the path will be a straight line.