✔ 最佳答案
Yes, you are right. We can apply this formula:
D = 1/2 C ρ A v²
where D = drag force
C = drag coefficient
ρ = density
A = cross-sectional area
v = speed
To find the terminal velocity, setting the drag force D equal to the gravity of the raindrop, i.e.
D = mg = ρ(4/3 π r³) g, where r is the radius of the raindrop
=> ρ(4/3 π r³) g = 1/2 C ρ π r² v²
=> v = √ [(8/3 r g ) / C]
Hence, v is proportional to the square root of the radius of the raindrop.
Therefore, the bigger raindrop has higher terminal speed.
Note: The drag coefficient, C, is only approximately constant for the raindrops of different sizes. The shape of the raindrops are only approximately spherical.