Introduction:
In this scenario, a man is standing at the top of a tower and he throws one object horizontally while he simply drops another object. The question is whether these two objects will reach the Earth at the same time or not.

Explanation:
To understand whether the two objects will reach the Earth at the same time or not, we need to consider the factors that affect their motion. These factors include the initial velocity, the force acting on the objects, and the presence of any air resistance.

Effect of Initial Velocity:
When the man throws the object horizontally, it means that the object has an initial velocity in the horizontal direction. This initial velocity causes the object to have a horizontal motion along with its vertical motion due to gravity. On the other hand, when the man simply drops the object, it has no initial velocity in the horizontal direction.

Effect of Force and Acceleration:
Both objects experience the same gravitational force while falling towards the Earth. The force of gravity causes them to accelerate in the vertical direction. The acceleration due to gravity is constant and equal to 9.8 m/s^2. Therefore, both objects experience the same acceleration.

Effect of Air Resistance:
In the absence of air resistance, both objects would fall with the same acceleration and reach the Earth at the same time. However, in reality, air resistance can affect the motion of objects. When the horizontally thrown object moves through the air, it experiences air resistance in the horizontal direction. This air resistance can slow down the object's horizontal motion, but it does not affect its vertical motion. On the other hand, the vertically dropped object experiences negligible air resistance since it is moving straight down.

Conclusion:
Considering all these factors, the horizontally thrown object and the vertically dropped object will reach the Earth at the same time. This is because both objects experience the same acceleration due to gravity in the vertical direction and any differences in their horizontal motion due to air resistance do not affect their vertical motion. Therefore, regardless of their initial horizontal velocities, both objects will fall towards the Earth with the same acceleration and reach the ground simultaneously.