Freely Falling Bodies


Any body is falling freely from some height(h) due to gravity is called freely falling bodies. This is best example of motion in vertically a straight line with uniform acceleration. How can we find out the freely falling bodies velocity, displacement and time taken ? We can find out using equations of motion. 
         
            Let us consider vertically upward direction taken as the positive Y-axis  and vertically downward direction taken as negative Y-axis. 
           So here freely falling bodies , 
                                                               a= -g
                                 Initial velocity (u)=0

                  
Equations

But in physics we have to taken if a= -g when a body is moving uniform acceleration vertically upward direction. a= -g  here '- 'represents the direction of acceleration of the body is opposite to the direction of acceleration due to gravity of the earth.  If a= +g when the body is moving uniform acceleration vertically downward direction. a=+g here '+' represents the direction of acceleration of the body is same the direction of acceleration due to gravity of the earth. 
             
           So for freely falling bodies a=+g                   Equations
The equation for the distance covered in nth second
                     hnth =g÷2(2n-1)

Note: 1) Air resistance is neglected  and the body is dropped near the earth surface.
2)The Acceleration due to gravity of the earth is always downward direction. It's magnitude is 9.8m/s2.


1) A body falling freely from 'Y' height. The time taken by the body to reach ground is 10 s then what is the height Y? (g=10m/s2)

2) An object is dropped from height A metre then it reached the ground in 8s. What is the velocity when it is touching the surface of the earth ?(g=10m/s2)

3) When an object is dropped from a height 40 metres then what is the velocity at 20m after the object dropped?(g=10m/s2) 

4) A body is falling freely with uniform acceleration near the surface of earth to be 10 m/s2. What is the velocity of the body at the end of 2 second of free fall ?


For solutions see below video 

1)A ball released from certain height H, it reaches the ground in time T. Where it will be from the point of release at a time 5T/6?

2)Two bodies x and y are made to fall freely from a height H and 2H at same instant then what is the difference between their final velocities? If V is the final velocity of x .

3)Time taken by a body falling from rest to cover the heights of X1 and X2 are respectively t1 and t2 then ratio of t1 and t2 is? 

4)A body dropped from a height H at time t =0  reaches the ground at time t1. The time taken by which it  would have reached a height H/2 is?


Solutions see below video

PRACTICE QUESTIONS FOR STUDENTS 

1)The time  of a freely falling body on reaching the surface of earth from a height h is given by?

2)A body is dropped from a tower height X metres and reaches time taken 10 seconds then what is height X?

3)The uniform acceleration near the surface of earth to be 10 metre per second square free fall.What is the velocity of a body at the end of 3
 seconds of free fall the initial velocity is zero?

4)A body is dropped from a height of 40 metres then what is the velocity at thirty years after the body dropped ?(acceleration of the body is 10 metre per second square )

5)A ball is dropped from a height. If it takes 5 seconds to cross the last 6 metres before hitting the ground then the height from which it was dropped ?(Acceleration of the body is 10 metre per second square )

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