.MOTION OF A BODY IN A RESISTING MEDIUM 888 



If R Ib. is the resistance of the air, then R - kv where k is a 

 constant and if m Ib. is the mass of the body. 



mg Rg = m x acceleration 



do 



tn -- = mg - kgo 



dv kg 

 Now 



m J m 



kot 



and the integrating factor is therefore e m 



qkl f okl 



Hence ve m = g\e m dt+ Const 



m ^r , r 

 = _ _j_ Const 



k 

 but when t = 0, v = 0, since the body falls from rest. 



Then = j + Const 



w 2 m 



Qtiri i^pm /> *n -, . _. __ 



re ~fc* A; 



It should be noticed that as becomes large, e m becomes 

 small, and therefore the velocity of the body tends to the limiting 



m 



value T-. 

 k 



j 

 XT cw* m 



NOW V = -j- = y- 



<// k 

 Integrating, s = -j- 



but when t = 0, s = 0, then = ^ + Const 



m 2 



d s -k( t+ -ji? m )-gk* 





