QN about physics plz help thx

Question

A raindrop of mass m is falling vertically through the air with uniform speed v. The raindrop experience a retarding force kv due to the air,where k is a constant.The acceleration of free fall is g.i know the expression for the kinetic energy of raindrop is m^3g^2/ 2k^2. but how to find this expression

Answer 1

First we should find the uniform speed, v.

Three forces act on the rain drop :

1) its weight, mg, downwards

2) force of buoyancy, upwards which we can ignore as in air medium it is very small due to very small density of air

3) retarding force kv, upwards

As the velocity is uniform, these forces must balance and ignoring the buoyant force

kv = mg

=> v = mg/k

=> kinetic energy

= (1/2) mv^2

= (1/2) m * (mg/k)^2

= m^3g^2/ 2k^2.