why does a ball take the same time to travel up and come down
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as the ball travels on its arc, air resistance is constantly being reduced, which means that it's maximum kinetic energy is reduced both the start and end of the trip down being lower than the trip up... The problem becomes more complex if you add a horizontal velocity component.
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Because going up suppose we start from speed U, then by equation v²-u²= 2as, we see that when falling down the final speed of ball will also be U... therefore ball starts and ends with same speed. Now with the equation v=u+at, we'll get t same for both upward and downward journey... you can check for any example
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