Question

2 A particle falling from rest in a vertical line in a medium with resistance kv per unit mass, k is a constant, v is the velocity at any time and position x, prove that it acquires a speed 9. -2kh 1 - e T is the terminal velocity given by a distance h, where in falling through T A particle projected upwards in the same medium with initial speed V, and returns to the point of projection with speed Vp . -2 -2 Prove that V + T

Answer 1

aatad is alling rm ret in a vegicd tiaa in medium usith istan.re kv E&D rebady Diograndthe freayplling -Pactide Ky triel peritier Mat a e uing the fquilibsinqun ma 2 dv KV V

YP dh V Kv2 hole goadng enbes om dv v O Sel ids on 2kvv dx 2K Limis Chage ar fulaws.

V2O ,3=Kv n 9- In 2kh -2Kh

Kv (1-2 К V 2кh e ruetion he pantick is pro iehed spoands and aetunn tuthpaint if projectien uiltnVR h metial ped

e spoand the he he KV m ma erhingth Equiliboim Tet grke dh dv v du dx vdy 2kdh 2K

-2kh Ln - 2V4 +2k 4 +2KG e. 2. 2K +2Kh V Con se the amula denived presioauy L-c2kh 2kh

uning_Equactin 2Kh 2 2kh 2 V2 2h. 2K h 2Kh R -2Kh 2kh VR2