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Message: [QUOTE="eebmg, post: 3249956, member: 7548"] Here is a solution which I think is slightly more general than [USER=7631]@Bigboote[/USER] which can be found at [URL unfurl="true"]https://www.xbats.com/blog/collisions-and-the-conservation-of-momentum.htm[/URL] Here, the energy conservation is not strictly satisfied and the loss of energy into heat is empirically approximated by a coefficient of restitution (e) taking into account a 'compressability or elasticity ' of the ball which connects the change in ball velocities to a change in bat velocity and gives the 'second' equation for the 2 variable problem. In fact elastic collisions (energy conservation) is satisfied in the case e=1 see [URL='https://en.wikipedia.org/wiki/Coefficient_of_restitution']Coefficient of restitution - Wikipedia[/URL] The formula they get (verified) is [ATTACH type="full" alt="45770"]45770[/ATTACH] This equation says the batted ball velocity ([I]v[/I]1a) depends on the mass of the ball ([I]m[/I]1) and bat ([I]m[/I]2), the elasticity of the ball ([I]e[/I]), the pitched ball speed ([I]v[/I]1b) and the bat swing speed ([I]v[/I]2b). However, keep in mind that [B][U]v1b is negative[/U][/B] since it is directed opposite the other velocities. What is interesting about this solution is that only if (m1-e*m2) <0 ; will the affect of increasing the pitched ball speed acts to increase the batted ball velocity. In the article, they say for a baseball, e ~ .55 so as long as m1 < m2*e or m2 > 2*m1 , increased pitch velocity gives increased exit velocity. This condition is clearly satisfied in real life. See next post [/QUOTE]

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