If the effects of the air acting on falling raindrops are ignored, then we can t

Question

If the effects of the air acting on falling raindrops are ignored, then we can treat raindrops as freely falling objects. (a) Rain clouds are typically a few hundred meters above the ground. Estimate the speed with which raindrops would strike the ground if they were freely falling objects. Give your estimate in m/s, km/h, and mi/h. (b) Estimate (from your own personal observations of rain) the speed with which raindrops actually strike the ground. (c) Based on your answers to parts (a) and (b), is it a good approximation to neglect the effects of the air on falling raindrops? Explain.

Explanation / Answer

a)

Intial velocity (u) = 0    acceleration due to gravity = g = +9.8m/s2 .

height of the clouds = h = hundred meters.= 100m

Use equation v2-u2 = 2aS.

                       v2= 2*g*h

                       v2 = 2*9.8*100

                       v = 44.27m/s.
                          =160km/h.
                          =99mi/h.
velocity of the rain drop is 20m/h.
from the above values we can conclude that air resistanceacting on the rain drops can be neglected

(b) Raindrops actually have a speed of about 1 m/s as they strike the ground.
(c) The actual speed at the ground is much less than the speed calculated assuming free-fall, so neglect of air
resistance is a very poor approximation for falling raindrops.
EVALUATE: In the absence of air resistance raindrops would land with speeds that would make them very
dangerous.

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