# Question #cc79c

##### 1 Answer

Nov 1, 2016

A falling object experiences two forces

- 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. - 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

Using (1) and (2) we get

Using equation for Newton's second law of motion we obtain