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What is free fall ? Write equations of uniformly accelerated motion for object falling freely.
Solution
The acceleration produced in the object due to gravitational force is called gravitational acceleration.
This acceleration is in downward direction.
If the air resistance is neglected, then this type of falling of object is said to be free fall. Here, acceleration is considered as negative gravitational acceleration.
This is also an uniformly accelerated motion.
By putting $v_{0}=0, a=-g, d=-h$ in the kinematic equations; we can derive equations for free fall.
$v=v_{0}+a t$
$\therefore v=-g t$
$d=v_{0} t+\frac{1}{2} a t^{2}$
$\therefore -h=-\frac{1}{2} g t^{2}$
$\therefore h=\frac{1}{2}g t^{2}$
$v^{2}-v_{0}^{2}=2 a d$
$\therefore v^{2}=2(-g)(-h)$
$\therefore v^{2}=2 g h$
$\therefore v=\sqrt{2 g h}$
