# Cosmic dust

A spherical comet of mass $$M=10^{14}~\text{kg}$$ and diameter is $$D=8~\text{km}$$, travelling at $$v_{0}=100~\text{km/s}$$ enters a cloud of stationary cosmic meteoroids (small rocks). The average density of the cloud is $$\rho= 1~\text{kg}/\text{m}^3$$. When a meteoroid impacts the comet it adheres to its surface. As a result the comet slows down and after traveling $$L=500~\text{km}$$ it exits the cloud. How much time in seconds does the comet spend in the cloud?

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