Problem: Calculate the speed a spherical rain drop would achieve falling from 5.00 km (a) in the absence of air drag (b) with air drag. Take the diameter of the drop to be 4 mm, the density to be 1.00x103 kg/m3, and the surface area to be πr2.

FREE Expert Solution

Terminal velocity of a falling object:

vt=2mgρCA, where ρ is the density of the medium, C is the drag coefficient, A is the frontal area of the falling object, m is the mass of the object, and g is the acceleration due to gravity. 

We'll also use the kinematic equation:

 vf2= v02 -2gy

(a)

In the absence of the air drag, the drop is falling freely.

Let the displacement downwards be in the negative y-axis. 

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Problem Details

Calculate the speed a spherical rain drop would achieve falling from 5.00 km (a) in the absence of air drag (b) with air drag. Take the diameter of the drop to be 4 mm, the density to be 1.00x103 kg/m3, and the surface area to be πr2.

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