This is one of the most important distinctions in physics. It is really important that you understand the difference between velocity and acceleration.

Sure, the ball has a higher velocity, but absolute value of the velocity does not affect acceleration one bit. Look at the definition of acceleration. It is the CHANGE in velocity divided by the CHANGE in time.

Consider two cars. One is moving at a constant velocity of 55 miles per hour east and the other is moving at a constant velocity of 35 miles per hour east. What are their accelerations? Well, let’s calculate the acceleration over a 1 second time interval.

The first car is traveling at a constant velocity of 55 miles per hour east. Thus, when we “start the clock,” it is traveling 55 miles per hour east. When we stop the clock one second later, it is still traveling 55 miles per hour east. What is the acceleration?

a = (change in v)/(change in t) = (55 – 55) / (1 – 0) = 0

The second car is traveling at a constant velocity of 35 miles per hour east. Thus, when we “start the clock,” it is traveling 35 miles per hour east. When we stop the clock one second later, it is still traveling 35 miles per hour east. What is the acceleration?

a = (change in v)/(change in t) = (35 – 35) / (1 – 0) = 0

Thus, both cars have different velocities but the EXACT SAME acceleration.

It is the same with the rock and the thrown ball. They each have different velocities, but the velocities are CHANGING at the same rate. Thus, they have the same acceleration – the acceleration due to gravity.