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Displacement of COM:Application

What is Termi...

Question

What is Terminal Velocity ? Derive an expression for Terminal Velocity.

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Solution

$w h e n a b o d y i s d r o p p e d f r o m a h e i g h t t h e n t e r m i n a l v e l o c i t y i s t h e h i g h e s t v e l o c i t y i t a t t a i n s i n f r e e f a l l . i f a n o b j e c t o f m a s s m i s f a l l i n g d o w n t h e n F = m g - F_{d} w h e r e F_{d} = d r a g f o r c e d u e t o m e d i u m r e s i s \tan c e = \frac{1}{2} ρ v^{2} A C_{d} w h r e ρ = d e n s i t y o f t h e m e d i u m t h r o u g h w h i c h t h e o b j e c t i s f a l l i n g A = p r o j e c t e d a r e a o f t h e o b j e c t C_{d} = d r a g c o e f f i c i e n t t h e r e f o r e m g - \frac{1}{2} ρ v^{2} A C_{d} = 0 v = \sqrt{\frac{2 m g}{ρ A C_{d}}} [A N S]$

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