If the effect of the air resistance acting on falling raindrops is 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 m/s, km/hr, and mi/hr? b.) From your own personal observations of rain estimate would strike the
ground if they were freely falling objects. Give your estimate in m/s, km/hr, and mi/hr, the speed with which
raindrops actually strike the ground. C.) Based onyour answers to parts (a) and (b), is it a good approximation
to neglect the effects of the air on falling raindrops? Explain.
it is really confusing I hope someone can help me with
a.) To estimate the speed at which raindrops fall, we can use the equation of motion for freely falling objects. The equation is:
s = ut + (1/2)at^2
where:
s = distance fallen
u = initial velocity (0 m/s, as the raindrops start from rest)
t = time taken to fall
a = acceleration due to gravity (approximately 9.8 m/s^2)
Since we are ignoring air resistance, we can assume that the acceleration due to gravity remains constant throughout the fall.
Given that rain clouds are typically a few hundred meters above the ground (let's assume 200 meters), we can determine the time taken for a raindrop to fall using the equation:
s = (1/2)at^2
200 m = (1/2)(9.8 m/s^2)t^2
Simplifying the equation, we get:
t^2 = (2 * 200 m) / 9.8 m/s^2
t^2 ≈ 40.82
t ≈ √40.82
t ≈ 6.39 s
Now we can find the speed of the raindrop using the equation:
v = u + at
v = 0 + (9.8 m/s^2)(6.39 s)
v ≈ 62.62 m/s
To convert this speed to km/hr, we can multiply by the appropriate conversion factor:
62.62 m/s * (3.6 km/hr / 1 m/s) ≈ 225.46 km/hr
To convert this speed to mi/hr, we can multiply by another conversion factor:
225.46 km/hr * (0.621 mi/hr / 1 km/hr) ≈ 140.25 mi/hr
Therefore, the estimated speed of raindrops in m/s is approximately 62.62 m/s, in km/hr it is about 225.46 km/hr, and in mi/hr it is roughly 140.25 mi/hr.
b.) For the speed at which raindrops actually hit the ground, we can estimate based on personal observations. This may vary depending on weather conditions, but let's assume a typical rain scenario.
From personal observations, it seems that raindrops fall at a slower speed compared to their initial speed due to the effects of air resistance. Let's estimate a slower speed of around 10 m/s.
Using the conversion factors from earlier, the estimated speed in km/hr would be:
10 m/s * (3.6 km/hr / 1 m/s) ≈ 36 km/hr
And in mi/hr:
36 km/hr * (0.621 mi/hr / 1 km/hr) ≈ 22.37 mi/hr
Therefore, the estimated speed at which raindrops actually hit the ground is approximately 10 m/s, 36 km/hr, and 22.37 mi/hr.
c.) Based on the answers from parts (a) and (b), it is evident that there is a significant difference between the estimated speeds of freely falling raindrops and the observed speeds upon reaching the ground.
The estimated speed without considering air resistance is much higher than the speed observed. The estimated speed is around 62.62 m/s, while the observed speed is only about 10 m/s. This difference suggests that air resistance has a substantial effect on the speed of raindrops.
Therefore, it is not a good approximation to neglect the effects of air resistance on falling raindrops. Air resistance plays a significant role in slowing down the raindrops, resulting in lower observed speeds compared to the speeds calculated without considering air resistance.