Although the force of air resistance is significant for most balls thrown with any reasonable speed, it is customary to neglect it in introductory physics because it is hard to calculate.
The force of gravity is directed toward the center of the Earth, but for thrown balls, the distance covered is small enough that the Earth is approximately flat over that distance, so the force of gravity is taken to be in a constant direction, downward.
These forces cause an acceleration of the ball in the direction of the total force, downward for the gravity part and backward for air resistance part. The acceleration is the magnitude of the force divided by the mass of the ball. This acceleration changes the initial speed and direction that the ball had at the instant of the throw, causing it to follow a curved path.
To experiment with these ideas and others click on the following link. It will take you to a virtual laboratory where you may experiment with initial velocities and forces.
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