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

Question

1. 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.)

Explanation / Answer

Since air resistance is dependent on velocity that when throwing the ball upward since both air resistance and gravity are applying force in the same direction the ball will more quickly come to a stop however since when the ball is dropping the force due to air resistance is opposing gravity the ball will take longer to travel the same distance back down.

For upward direction the net acceleration is gravity+air drag (-g-a) acting downwards. Let us suppose it take t1 to reach maximum height of h.

Then while coming down the net acceleration is gravity-air drag (g-a) acting downwards. Since acclearation has decreased than previous vales hence t2 (time to reach ground from maximum height) will be higher than t1.

Therefore, time of flight for the upward journey is less than the time of flight for the downward journey.

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