## Saturday, February 4, 2017

### Equations of Motion for Vertically Thrown up body

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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