The ball always falls back into the moving cannon because of the principle of inertia and the force of gravity acting on the ball.
Firstly, let's consider the concept of inertia. The car and the ball are initially at rest, so they have zero velocity. When the car receives a push and starts moving horizontally with a constant velocity, according to Newton's first law of motion, the ball tends to maintain its state of rest or motion in a straight line. This means that as the car moves forward, the ball will also move forward with it.
Now, let's focus on the vertical motion of the ball. When the pin is pulled and the ball is launched vertically, it experiences an upward force due to the spring-loaded cannon. As a result, the ball gains upward velocity and starts moving against the force of gravity.
However, gravity is still acting on the ball, pulling it downward. This downward force gradually slows down the upward motion of the ball until it eventually comes to a stop and starts falling back down towards the Earth.
During this upward and downward motion, the horizontal velocity of the car remains constant. As a result, when the ball falls back down, it still has the same horizontal velocity as the car. The ball and the car are essentially moving together, and due to the inertia of the ball, it falls back into the moving cannon.
In simpler terms, the ball falls back into the moving cannon because both the ball and the car have the same horizontal velocity, and the force of gravity acting on the ball does not affect its horizontal motion. Therefore, regardless of the upward and downward motion of the ball, it maintains the same horizontal velocity as the car and falls back into the cannon.