A rain drop of mass m, starts falling from rest and it collects water vapour and grows. If it gains lambda kg/s, find its velocity at any instant.

A rain drop of mass m, starts falling from rest and it collects water

1.	A rain drop of mass m, starts falling from rest and it collects water vapour and grows. If it gains lambda kg/s, find its velocity at any instant.
Answer» Solution :`(d)/(dt) (MV) = mg , (dm)/(dt) = lambda or m= lambda t + K` where K is a constant when t=0 , `m=m_0 :. m=m_0 + lambda t ` so , ` (d)/(dt) {(m_0 + lambda t)v} = (m_0 + lambda t ) g` Integrating , `(m_0 + lambda t) v= int (m_0 + lambda t) g dt = (m_0 t + ( lambda t^(2))/(2) ) g + C ` where C is constant when t =0, v=0 ` :.` C =0 `:. (m_0 + lambda t) v = ( m_0 t + ( lambda t^2)/(2)) g , v=(g(m_0 t + (lambda t^2)/( 2)))/(m_0 + lambda t ) =(g (t+ (lambdat^(2))/(2m_0)))/( 1 + (lambda t)/( m_0))` This mean VELOCITY changes w.r.t . time