It is well known that a rain drop falls under the influence of the downward gravitational force and the opposing resistive force. The latter is known to be proportional to the speed of the drop, but is otherwise undetermined. Consider a drop of mass 1.0g falling from a height of 1.00km. It hits the ground with a speed of `50.0ms^(-1)` (a) What is the work done by the gravitational force ? (b) What is the work done by the unknown resistive force ?

Explanation

Considering that the drops is initially at rest on the cliff , intial velocity , u = 0
Mass , m = 1.00 g = 0.001 kg
Final velocity , v = 50 m/s
Height , h = 1.00 km = 1000 m
Increase in kinetic energy of the drop is
`= 1/2 mv^(2) - 1/2 "mu"^(2)=1/2mv^(2)`
` =1/2 xx 0.001 xx (50)^(2) = 1.25 J `
If ` g = 10 m//s^(2)` , work done by gravitational force is
`W_(g)= mgh = 0.001 xx 10 xx 1000 = 10 J `
If `W_(r)` is the work done by the resistive force , then
`K = W_(g)+W_(r)`
` rArr W_(r) = K-W_(g) = 1.25 - 10 = - 8.75 J`