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The rain drop of mass 1 g, starts with zero velocity from a height of 1 km. It hits the ground with a speed of 5 m/s. The work done by the unknown resistive force is _______ J.
(take g = 10 m/s$$^2$$)
Use work-energy theorem:
$$W_{gravity}+W_{resistive}=\Delta K$$
given:
$$m=1g=10^{-3}kg$$
h=1 km=1000 m
u=0,v=5 m/s
step 1: work done by gravity
$$W_g=mgh=10^{-3}\times10\times1000=10J$$
step 2: change in kinetic energy
$$ΔK=\frac{1}{2}mv^2=\frac{1}{2}\times10^{-3}\times25=0.0125J$$
step 3: resistive work
$$10+W_r=0.0125$$
$$W_r=0.0125-10=-9.9875J$$
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