Equations of motion for a vertically
thrown up body
Thus the velocity of the body keeps on
decreasing and at a particular height, its velocity becomes zero and that
height is said to be the maximum height that the body can go and the time taken
to reach that maximum height is called time of ascent.
Acceleration in this
case is acceleration due to gravity which is constant and it shall be treated
as negative as the velocity of the body keeps on decreasing with respect to
time. Taking this into consideration, we can rewrite the four equations of
motion for a freely falling body. It is proved that the velocity with you
project the body vertically up is the velocity with which it comes back to the
same point of projection but in the opposite direction. It is also proved that
when air resistance is ignored, time of ascent is equal to the time of descent.
Time of Ascent and Decent with Air resistance
As it is mentioned earlier time of
ascent of a vertically thrown up body is equal to the time of descent of a
freely falling body. The above mentioned statement is true only when air
resistance is ignored. But in real life air resistance is there and if that is
taken into consideration, time of ascent is different from time of descent. Air
resistance offers a force against the motion and it always acts opposite the
motion. Thus when the body is thrown up, both gravitational force and resistance
force acts against the motion. When the body is coming down, gravitational
force acts in down ward direction but air resistance acts opposite to the
motion and that is in upward direction. Thus we can find the effective
acceleration in both the cases and find the the relations between time of
ascent and descent as shown in the video below.
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