FREE FALL

Free Fall is when an object is allowed to fall freely under the earth's gravitational pull. In free fall  AIR RESISTANCE is negligible,all objects fall freely and have the same acceleration,g. Although the acceleration due to gravity is considered constant it tends to vary slightly over the earth since the planet is not a perfect sphere. The value of g is generally taken to be 9.81m/s^-2, often approximated to 10 m/s^-2. this means that the velocity of a free-falling body increases by 10 m/s^-1 every second. However, at the North Pole the value may be as high as 9.84 m/s^-2 and at the equator as low as 9.78 m/s^-2.




When a Body is thrown up, ITS VELOCITY DECREASES BY 10 m/s^-1 EVERY SECOND. (Physics Insights book by Pearson Education South Asia PTE LTD. Copyright 2004)

 The motion of an object in free fall can be described by four kinematic equations. The kinematic equations that describe any object’s motion are:

EXAMPLE
The graph shows how the velocity of a stone varied from the moment that it was thrown vertically upwards in air. The Velocity is taken to be positive when the stone was going upward and negative when the stone fell. The time taken for the stone to reach the highest point is the time when the instantaneous velocity of the stone is zero.


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GALILEO"S EXPERIMENT

Galileo, tried to convince people that our numerical integrator is accurate, by dropping two balls from the tower. One ball follows the analytical equation of free-fall motion while the other one is simulated by our particle system. His goal is to show that they reach the ground at the same time. He implemented two numerical integrator's to demonstrate that one of them yields the same motion as the analytical solution, while the other does not.

He used trapezoidal method for the first integrator and showed that it gives the same motion as the analytical solution. For the second integrator he used Euler's method and showed that the resulting motion has a delay.(http://abhijeetdani.com/particle_system.html)