Rain clouds often appear to move quickly because the wind speeds are significantly faster at higher altitudes.
Here's a more detailed explanation:
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Wind Speed and Altitude: The higher you go in the atmosphere, the faster the wind typically blows. This is due to factors like reduced friction from the Earth's surface and different pressure gradients at higher altitudes. Rain clouds, being suspended in the atmosphere, are carried along by these high-speed winds.
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Composition of Clouds: Rain clouds are primarily made up of water vapor and water droplets. These are relatively light and easily influenced by wind currents.
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Impact of Wind: The wind acts as a force pushing the clouds along. The stronger the wind, the faster the clouds will move. You are observing the effect of stronger winds aloft pushing these lighter-than-air structures across the sky.
In essence, the perceived fast movement of rain clouds is largely attributed to the increased wind speeds at higher altitudes.