# When we throw a ball vertically upward with any force, is the time to reach the highest point equal to the time to reach the ground?

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### 1 Answer

The answer to a question like this depends on the conditions of the problem. Under normal, Earth-like conditions the answer would have to be "no" for the following two reasons:

The person throwing the ball will release it above the ground. It might take the same amount of time to reach the highest point and to return to the height from which it was released. However, unless the person is standing in a hole when he throws the ball, it will take longer for the ball to continue and eventually strike the ground.

Also, the ball will experience air resistance which means its velocity on the return trip will be less than that with which it is initially launched and consequently it will take longer to get back down.

However, in the world of Physics' problems we usually make some assumptions to "simplify the problem". For example, we assume that the ball is experiencing free fall once it leaves the hand of the thrower and consequently there is no air resistance to influence the flight of the ball. We might also assume that the distance from the height of release to the ground is negligibly small and so the increase in distance to reach the ground may be ignored.

By making these two assumptions, we can argue from the symmetry of constant acceleration problem (it is in the form of an inverted parabola) that the time of flight to the highest point will equal the time of flight for the return trip.