### The statement in the text

*C. The ball immediately after its impact with the bat, moving skyward at an angle of 42 degrees and with an initial velocity estimated at 500 feet a second or nearly six miles a minute--faster than any express train travels.*
### My response

There are two errors in this statement. The most egregious error is the claim that the ball leaves the bat at 500 ft/s (equivalent to 341 mph or 5.7 miles/min). That is just not possible. In fact, I estimate that a ball hit at such an angle and such a speed would travel nearly 900 ft. No one has ever claimed to have seen a baseball hit that far. In fact, if one looks at batted ball speeds using modern technologies from MLB games (HITf/x, TrackMan), one finds the mean speed for home runs is about 100 mph, with the distribution dropping off sharply for higher speeds, with essentially no balls hit harder than 120 mph.
Not only is such a high batted ball speed (BBS) not observed in practice, it would seem to be physically impossible, given what we know about the **physics of the ball-bat collision**. It is very straightforward to compute a pretty good upper limit on BBS. First, for a typical MLB wood bat and baseball, the BBS for a squarely hit ball on the sweet spot of the bat follows the formula BBS=0.2*(pitch_speed)+1.2*(bat_speed). With a pitch speed of 85 mph as it crosses home plate, corresponding to about 10 mph higher at release, and a bat speed of 70 mph, we get BBS=101 mph, quite typical of a home run or any other hard-hit ball in MLB. Launched at 30 degrees, such a ball would travel about 400 ft.

Now let's play around with those numbers a bit to see how we can get a higher number. Suppose the Babe used a much heavier bat, say 48 oz or about 50% higher than typical, but still keeping the same bat speed. Then the 0.2 and 1.2 become 0.29 and 1.29, respectively, resulting in BBS=114 mph. We're still not even close. So, let's suppose the Babe could actually swing the bat at an astounding 90 mph, a nearly 30% increase over the 70 mph, corresponding to 67% more energy supplied by the batter to the (already quite heavy) bat or to 2.5 times the energy supplied to a typical bat. We then find BBS=140 mph. I think we can take this as an extreme upper limit on how hard a baseball can be hit by an MLB batter. Launched at 30^{0}, such a ball would travel over 550 ft. And it is not even close to the 341 mph claimed by the author. 'Nuf said.

Finally let's take a look at the 42^{0} launch angle. In a vacuum (i.e., without the effects of air drag and lift), the optimum launch angle is 45^{0}. In real life, it is more like 30^{0}, as seen both "theoretically" and from MLB data.

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