To be fair, a light ball is exactly where my estimate is known to be least accurate. Let’s consider, rather, a ball with a density of 1 - one that neither floats nor sinks in water. (Since, in my experience, many things sink in water and many, but not quite as many, things float in it, I think it makes a reasonable guess for the average density of all possible balls). Then you have m=0.0655kg, and thus:
...okay, if it was falling in a vacuum it would have reached that speed, but it’s had air resistance all the way down, so it’s probably not even close to that. (And it it had been dropped from, say, 240m, then I would have calculated a value of close on 70 m/s, which would have been even more wildly out).
So, I will admit, it turns out that mass is a good deal more important than I had expected—also, air resistance has a larger effect than I had anticipated.
To be fair, a light ball is exactly where my estimate is known to be least accurate. Let’s consider, rather, a ball with a density of 1 - one that neither floats nor sinks in water. (Since, in my experience, many things sink in water and many, but not quite as many, things float in it, I think it makes a reasonable guess for the average density of all possible balls). Then you have m=0.0655kg, and thus:
v = sqrt( 2 0.0655 9.8 / (1.2 0.00196 0.47)) = 34.0785 m/s
...okay, if it was falling in a vacuum it would have reached that speed, but it’s had air resistance all the way down, so it’s probably not even close to that. (And it it had been dropped from, say, 240m, then I would have calculated a value of close on 70 m/s, which would have been even more wildly out).
So, I will admit, it turns out that mass is a good deal more important than I had expected—also, air resistance has a larger effect than I had anticipated.