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When an object is thrown vertically downward, its initial velocity can be determined using the equation v = u + gt, where v is the final velocity, u is the initial velocity, g is the acceleration due to gravity, and t is the time it takes for the object to fall. In the given scenario, if the object hits the ground with a velocity of 10.0 m/s after falling for 0.880 s, we can calculate the initial velocity. The acceleration due to gravity on Earth is approximately 9.8 m/s^2. By rearranging the equation, u = v - gt, we find that the object was initially released with a velocity of u = 10.0 m/s - (9.8 m/s^2)(0.880 s) = approximately 0.136 m/s.