In real life condition, time of ascent of a freely falling body under gravity is equal to time of descent of that body or not? Please define.

Question

anonymous · Answer

Time of ascent will not equal time of descent in real life due to the effect of air resistance.  When the object is travelling upwards the forces acting on it are different than when it is in descent.  While travelling upwards, gravity and air resistance both act in the downward direction.  When the object is travelling downwards, gravity acts downwards but the air resistance acts in the upward direction (it retards the motion of the object).  Since there is an asymmetry in the up/down motion of the object, we expect the travel times to be different.

maheshmeghwal9 · Answer

ya but which time is greater & why?

anonymous · Answer

what are your thoughts on it?

maheshmeghwal9 · Answer

Answer is that time of descent is greater but why?

anonymous · Answer

Best to try showing it by calculation

maheshmeghwal9 · Answer

ya but how I don't know.

anonymous · Answer

Unfortunately I have to go right now, I'll come back and post this later

maheshmeghwal9 · Answer

np:)

anonymous · Answer

Ok, one way to see this is in terms of mechanical energy.  Recall that if there is no air resistance, mechanical energy (the sum of the potential and kinetic energy) is constant.  This means that if a body ascends through a point y with a velocity v, it will have  velocity -v when the body descends through the same point y on the way down.  Now in your problem mechanical energy is not conserved.  It will be lost through friction with the air.  This means our body will have maximum mechanical energy (all of it in the form of kinetic energy) when it begins it's ascent with initial velocity v0 and subsequently lose some mechanical energy as the object ascends.  Now when the object reaches the top of it's flight, it has no kinetic energy and all its energy which is left is in the form of potential energy.  This is of course less than the initial total mechanical energy we had when the object started out because some has been lost due to air friction.  So, if an object passed through a point y on the way up with a speed u, then it will pass through y again on the way down with a speed v where u>v.  This is true for all points y.  Therefore, the time it takes to travel the same distance will be greater for the descent than the ascent of the object.