Freely Falling Body

Important Conclusions from above Equations:

1) From eq(f) ,  i.e., the distance fallen in time t,2t,3t,.........etc.will be in the ratio \( 1^2 ,2^2 ,3^2 ,.....etc \).
    Example: ratio of the distance travelled in 1second, 2seconds, 3 seconds ,.....is \( 1^2 ,2^2 ,3^2 ,..... \)            
2) From the equation sn \( = \frac{1} {2}g(2n - 1) \), For any nth second of travel of freely falling body the ratio of the distances travelled in the 1^st second ,2^nd second, 3^rd second,.....is 1:3:5:7:........
3) From the equation v=gt, ratio of the velocities acquired at the end 1 second, 2 seconds, 3 seconds ,.....is  1:2:3:4:........
4) From the equation \( h = \frac{1} {2}gt^2 \), ratio of the times taken to travel 1st metre, 2nd meter, 3rd meter.........is \( \left( {\sqrt 1 - \sqrt 0 } \right):\left( {\sqrt 2 - \sqrt 1 } \right):\left( {\sqrt 3 - \sqrt 2 } \right):....... \) 
5) A freely falling body travels a distance S₁ in the first n seconds and a distance S₂ in the next n seconds,then S₁:S₂=1:3
6) If a body is dropped from height h above the ground ,it reaches the ground after time t=\( \sqrt {2h/g} \) On reaching the ground its velocity is \( \sqrt {2hg} . \) Average velocity of the body this motion is \( \sqrt {gh/2} . \)
7) If a body dropped from height h reaches the ground after time ‘t’,its final velocity is gt and average velocity during this motion is gt/2
8) A body dropped from height ‘h’ reaches the ground after certain time.After half of the time its height above the ground is 3h/4.
9) A body dropped from certain height reaches the ground after time ‘t’.If would cover exactly half of this distance after time \( t/\sqrt 2 \)