Final answer:
The statement is false; the acceleration due to gravity is always negative in the upward-positive coordinate system because it is always directed downward, regardless of the projectile's direction of travel.
Step-by-step explanation:
The statement that the acceleration of a projectile fired upward at an angle is positive while the object is going upward and negative while the object is going downward is false. In two-dimensional projectile motion, such as that of a football or a firework shell, the only acceleration acting on the projectile is due to gravity (assuming air resistance is negligible). This acceleration is constant and points downwards towards the Earth.
Therefore, regardless of whether the projectile is rising or falling, the acceleration due to gravity remains in the same direction - vertically downward. Defining the positive direction to be upward, the acceleration due to gravity is always negative because it is always directed downward. The vertical component of the velocity of the projectile will be positive as it rises and negative as it falls, but the acceleration, which is represented by gravity, does not change direction; it is always negative in our chosen coordinate system because gravity always pulls the projectile downwards.
Furthermore, the x-component of the acceleration of a projectile is 0, since the acceleration due to gravity acts only in the y (vertical) direction.