In windless weather, when the pilot is shooting training, "the observer on the ground sees that the trajectory of the projectile is a curve".

From the aircraft reference system, it is a straight line, or more accurately, a straight line trajectory of vertical drop; Seen from the ground reference system, it is a parabola.

Let's assume that the reference system on the ground is a stationary reference system.

First of all, on the plane. According to the aircraft reference system, he doesn't think he is moving. So throwing things down on an airplane is exactly the same as throwing things down from a static height. So on the plane, the trajectory of the object is a straight line.

In addition, from the ground, it is considered that when an object just leaves the plane, it has an initial velocity with a horizontal component (this initial velocity is because the plane is flying relative to the ground). Generally speaking, it won't go down vertically, but there will always be another horizontal component). The trajectory of an object with initial velocity of horizontal component moving freely in gravity field is a parabola, so it is a curve.

In fact, you can think about this problem again: I throw a small ball downstairs from a tall building, and the trajectory of the ball looks like a straight line to people standing still downstairs (I will think so); The person sitting in the car is moving at a constant speed (horizontally) relative to me. It seems that the trajectory of the ball is parabolic. These two questions are actually exactly the same.