As the ball travels upward its velocity will constantly decrease due to the downward effect of gravity acting on the ball. Eventually the velocity of the ball will reach a value of zero at the highest point of the ball's flight. Then the ball will start falling back to earth, gaining speed due to the influence of gravity on the ball. When the ball is moving upward, earth's acceleration due to gravity, 9.8 m/s/s is acting against the ball, while on the return to earth, that same 9.8 m/s/s is causing the velocity of the ball to increase.

Because the ball is moving in a parabolic motion, ignoring any effects due to air resistance and wind, the velocity of the ball when it returns to the starting point has the same magnitude, 7.5 m/s, but because velocity is a vector, with both magnitude and direction, the new velocity is -7.5 m/s.

Because you defined up as positive initially (+7.5 m/s), that means that velocity in the opposite direction (down in this case) must be negative.

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