Answer
(a) equal to
(b) III
Work Step by Step
(a) As the two balls are identical and thrown from the same height, the change in gravitational potential energy is the same. According to the law of conservation of energy, the change in kinetic energy is also the same. Thus, the change in kinetic energy of your ball is equal to the change in kinetic energy of your friend's ball.
(b) We know that the best explanation is option (III) -- that is, the change in gravitational potential energy is the same for each ball, which means the change in kinetic energy must be the same also.
