I think this is a simplified example. 45 degrees is NOT the optimal angle in this case.
45 degrees is only optimal when you are maximising range over flat ground. I think you could hit the ball a little slower and still clear 'the green monster'.
@imaginenoreligion Yes, the optimal angle is 0.73196 radian (41.9382 degrees), and the required speed then becomes 32.3595ms^-2, rather than the 32.5 Sal concludes in the second part when he solves for 45 degrees. It's not a very significant difference.
wolfram alpha: y = s*(x/(sin(θ)*s))*cos(θ) - (g*(x/(sin(θ)*s))^2)/2 where x = 96, y = 10.3, g = 9.8 -> 10.3 = 96 cot(theta)-(45158.4 csc^2(theta))/s^2 wolfram alpha: minimum s for 10.3 = 96 cot(theta)-(45158.4 csc^2(theta))/s^2
@puddingpimp of course in this case the difference is ~0.4%, smaller than other effects like drag that need to be taken into account in the real world.
Would humidity play any real role in the calculations? Would you need more force to hit the ball as far if the humidity was 90% compared to 10%? Just wondering if there is a significant difference in the amount of energy needed to hit the ball the same distance.
I hope that once you finish with these new elementary classical physics videos that you move to more advanced classical mechanics.. and maybe even quantum mechanics?
ahh fenway. made learning a bit more interesting but still when does a baseball player ever think of all this when he's hitting? haha anyways good video
I'm actually curious IF 45 degrees is the ideal angle. In this case, the angle comes into play both to clear the green monster and to counter gravity. Though, as we know from ballistics, at a high enough velocity and a target close enough less force is required with a flatter trajectory. I'm quite sure that with some proper optimization the actual angle would be closer to 40. Of course, that is still not considering any spin the ball may have.
I like the idea of adding CS, But a Virtual Training Jacket Or Certificates that you could print would be awesome. This would be Invaluable to Those without access to Traditional Education. If you would like to see the A.C.E. consider KA send an E-mail to: comments@ace.nche.edu
@cosmosgato you should look up "Laplace's demon" on wikipedia!
ReplyDeleteI never knew the Green Monster was that high! Would the same ideas apply if I was, say, shooting free throws or kicking field goals?
ReplyDeletego soxxxxxxxxxxxxxxxxxxxxxxxxxxx
ReplyDeleteI think this is a simplified example. 45 degrees is NOT the optimal angle in this case.
ReplyDelete45 degrees is only optimal when you are maximising range over flat ground.
I think you could hit the ball a little slower and still clear 'the green monster'.
8:00 you didn't write delta t *trollface*
ReplyDelete@mnmmoose14 LOL @ "trollface" ahahahah
ReplyDelete@mnmmoose14 LOL @ "trollface" ahahahah
ReplyDelete@imaginenoreligion Yes, the optimal angle is 0.73196 radian (41.9382 degrees), and the required speed then becomes 32.3595ms^-2, rather than the 32.5 Sal concludes in the second part when he solves for 45 degrees. It's not a very significant difference.
ReplyDeletewolfram alpha: y = s*(x/(sin(θ)*s))*cos(θ) - (g*(x/(sin(θ)*s))^2)/2 where x = 96, y = 10.3, g = 9.8
-> 10.3 = 96 cot(theta)-(45158.4 csc^2(theta))/s^2
wolfram alpha: minimum s for 10.3 = 96 cot(theta)-(45158.4 csc^2(theta))/s^2
@puddingpimp of course in this case the difference is ~0.4%, smaller than other effects like drag that need to be taken into account in the real world.
ReplyDelete@UltraMaXAtAXX Yes they would, but when shooting free throws, the optimal angle is not 45 degrees because its better to have arc on the ball
ReplyDeleteWould humidity play any real role in the calculations? Would you need more force to hit the ball as far if the humidity was 90% compared to 10%?
ReplyDeleteJust wondering if there is a significant difference in the amount of energy needed to hit the ball the same distance.
I hope that once you finish with these new elementary classical physics videos that you move to more advanced classical mechanics.. and maybe even quantum mechanics?
ReplyDelete@cosmosgato Heisenberg uncertainty principle, so no.
ReplyDelete@Zellonium Yes, I could have very much used the help!!
ReplyDeleteFirst time Ive ever fallen asleep watching youtube :)
ReplyDeleteahh fenway. made learning a bit more interesting but still when does a baseball player ever think of all this when he's hitting? haha anyways good video
ReplyDeleteKhan, you forgot to add a randomization factor (beta/alpha) that takes into account the additional force due to the use of STEROIDS by athletes.
ReplyDeletei'm so glad i'm a poly sci major
ReplyDelete@hitch4645 until you try to find a job
ReplyDelete@LuckyCharms432 touche
ReplyDelete@Cascade3891 lol.
ReplyDeleteso boring....wow sports
ReplyDeleteI'm actually curious IF 45 degrees is the ideal angle. In this case, the angle comes into play both to clear the green monster and to counter gravity. Though, as we know from ballistics, at a high enough velocity and a target close enough less force is required with a flatter trajectory. I'm quite sure that with some proper optimization the actual angle would be closer to 40. Of course, that is still not considering any spin the ball may have.
ReplyDeleteI like the idea of adding CS, But a Virtual Training Jacket Or Certificates that you could print would be awesome. This would be Invaluable to Those without access to Traditional Education. If you would like to see the A.C.E. consider KA send an E-mail to: comments@ace.nche.edu
ReplyDelete