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## Homework Statement

A particle of mass m falls from rest from height h above the ground. The retarding force per unit mass due to air resistance is kv^2 where k is a constant and v is the velocity of the particle

a) write and simplify the equation of motion for the particle

b) find an expression for the velocity with which the particle reaches the ground

c) if h is very large, determine the expression for the velocity of the particle

d) explain what happens to the velocity when h is very large

## Homework Equations

## The Attempt at a Solution

a) i thought a particle falls with equation F=ma and the air resistance works against this so F=ma-kv^2

b) no idea just yet :(

c) when h is very large there is an equilibrium in net force and so terminal velocity is reached

terminal velocity = √2mg/pA(cd)

where p=density A=area of object cd=drag coefficient m=mass g=gravity

d) pretty much covered in part c) an object stops accelerating because the force of gravity and the air resistance are in equilibrium