Question

Acceleration of a projectile relative to another projectile is

Answer 1

The mentioned question is of projectiles in relative motion. We must first be clear about the projectile motion, the forces and direction of acceleration on objects in uniform projectile motion. Projectile motion is the motion of an object when it is obliquely projected from the Earth’s surface into air under the effect of only acceleration due to gravity. Comparing acceleration of projectiles in relative terms will yield the answer.

Complete answer:
When a projectile is in air it is acted upon by only acceleration due to gravity that too acts downward opposite to velocity in the vertical plane. In horizontal plane velocity remains constant as there is no force or resistance in horizontal plane.
If we throw two projectiles ($P_1$ and $P_2$) simultaneously or in a differential time frame we will notice that:
Both projectiles will follow the same mechanism of motion i.e. will be acted by only acceleration due to gravity and that too only in a downward direction. As both projectiles will have the same acceleration so when we notice acceleration of another projectile ($P_2$) by virtually imagining yourself on the present projectile ($P_1$) you will notice zero acceleration in that projectile $P_2$.
Numerically we can express acceleration of this relative projectile motion as:
Relative acceleration (a) = $-g_1-(-g_2) = 0$
$g_1$ = acceleration of projectile $P_1$
$g_2$ = acceleration of projectile $P_2$
Therefore, Acceleration of a projectile relative to another projectile is zero.

Note:
As the projectile doesn't have any acceleration or force acting in the horizontal plane, it will have a constant velocity in the horizontal plane. Relative acceleration of the projectiles is zero, i.e. relative velocity of the projectiles will be constant. Hence, the path of a projectile relative to another projectile is a straight line.