Final answer:
The velocity of the ball when it returns to the thrower's hand is equal to the initial velocity (option a) but in the opposite direction, due to the constant downward acceleration of gravity.
Step-by-step explanation:
The question involves a scenario where a ball is thrown straight upward and then falls back to the thrower's hand, which is an example of one-dimensional vertical motion under the influence of gravity. In such a case, when dealing with an ideal situation ignoring air resistance, the velocity of the ball when it returns to the thrower's hand should be equal to the initial velocity, but in the opposite direction since the velocity changes direction due to gravity acting on the ball.
All throughout the ball's journey, the acceleration due to gravity remains constant and points downward towards the center of the Earth, affecting the ball both on its way up and on its way down. The momentary velocity of the ball is zero at the peak of its trajectory, where it changes direction before descending.
To summarize, the correct answer to the student's question is (a) Equal to the initial velocity.