Question #cc79c

A falling object experiences two forces

1. Force due to gravity.
   A downward force directed towards center of earth on the mass #m#.
   #F_g=mg# .....(1)
   where #g# is acceleration due to gravity.
2. Drag force due to air resistance.
   A force acting opposite to the direction of motion of the falling object. As such it is an upwards force slowing down the falling body.
   Drag force #F_{D}# depends on the the size, shape, and speed of the object. It also depends on physical properties of air and is given by the expression
   #F_{D}=\frac {1}{2}\rho \v^{2}C_{D}\A# .....(2)
   where #rho# is the density of air, #v# is velocity of the object relative to air, #A# is the area of cross section and #C_{D}# is the drag coefficient which is a dimensionless number.

Therefore, net force #F_"net"# acting on the falling body is
#F_"net"=F_g-F_{D}#
Using (1) and (2) we get
#F_"net"=mg-\frac {1}{2}\rho \v^{2}C_{D}\A#

Using equation for Newton's second law of motion we obtain
#a_"net"=F_"net"/m#
#=>a_"net"=(mg-\frac {1}{2}\rho \v^{2}C_{D}\A)/m#
#=>a_"net"=g-\frac {1}{2m}\rho \v^{2}C_{D}\A" ms"^-2#