In our simple treatment of freefall problems, air resistance is ignored. The res

Question

In our simple treatment of freefall problems, air resistance is ignored. The result is that the upward velocity at any point is equal to but opposite that of the downward velocity. Hence, the time to rise equals the time to fall. But when the initial speed of the ball is high enough, air resistance cannot be ignored.

Air resistance always opposes the direction of motion. Taking air resistance into account, will the time of flight for the upward journey be the same, less, or more than the time of flight for the downward journey? Be sure to defend your answer! (The solution to this puzzle has interesting implications for the question concerning how dangerous is a bullet returning to the earth after it has been fired directly upward.)

Taking air resistance into account, will the time of flight for the upward journey be the same, less, or more than the time of flight for the downward journey? Be sure to defend your answer!

Explanation / Answer

When ball is moving upward, air resistance will act downward and hence net acceleration downward will be more. ( g + acceleration due to air resistance)

When ball is moving downward, air resistance will act upward and hence net acceleration downward will be less. ( g - acceleration due to air resistance)

we can thus say that the acceleration during the upward journey of the ball is larger in magnitude than the downward journey.
Acceleration is nothing but rate of change of velocity. This is larger when the ball is moving upward than when it is moving downwards. Therefore the time for the journey (upward or downward) depends inversely on the magnitude of acceleration.
So, for the upward motion the time of flight will be less than downward motion
Answer: less

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