6. A water droplet falling in the atmosphere is spherical. Assume that as the droplet passes through a cloud, it acquires mass at a rate proportional to kA where k is a constant (k>0) and A is its cross-sectional area. Consider a droplet of initial radius ro that enters a cloud with a velocity vo. Assume no resistive force and show (a) that the radius increases linearly with the time, and (b) that if ro is negligibly small then the speed increases linearly with the time within the cloud.
6. A water droplet falling in the atmosphere is spherical. Assume that as the droplet passes through a cloud, it acquires mass at a rate proportional to kA where k is a constant (k>0) and A is its cross-sectional area. Consider a droplet of initial radius ro that enters a cloud with a velocity vo. Assume no resistive force and show (a) that the radius increases linearly with the time, and (b) that if ro is negligibly small then the speed increases linearly with the time within the cloud.
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Transcribed Image Text:6. A water droplet falling in the atmosphere is spherical. Assume that as the droplet
passes through a cloud, it acquires mass at a rate proportional to kA where k is a
constant (k>0) and A is its cross-sectional area. Consider a droplet of initial radius ro
that enters a cloud with a velocity vo. Assume no resistive force and show (a) that the
radius increases linearly with the time, and (b) that if ro is negligibly small then the
speed increases linearly with the time within the cloud.
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