alpha's do matter, even if they are from a table. If they both had same materials, hence same alphas, that ring will never come off! Length initial of sphere equals .0005 times Length initial of ring added to length initial of ring. can you take it from here?
\frac{\partial f}{\partial z} = -3x^2z^2 = -3x^2z^2 + \frac{\partial h}{\partial z} \Rightarrow h(z) = 0
Im having trouble with latex, but your partial f over partial z which is -3x^2z^2 = -3x^2z^2 + partial h over partial z. so, h(z) = 0=g(y,x)
okay so, you start out with kinetic energy of the bullet then you hit the wood of certain mass, that slows down the bullet, but it slows down by raising the wood and bullet up some hight. then after that the bullet comes out of the wood at lower kinetic energy thus comes out slower then...
what material is the sphere and what material is the ring? What does that tell you about alpha value for each one? also on started out at what length in regards to the other?
The change plus the initial value for each material should equal each other right?
You can have a vector as long as it begins from a point and end at a another point right? Thats what I get from vector formulas. It is not required for a vector to start at the an origin right? Is that what you mean?
use alpha for both because the size of sphere is proportional to the diameter. as the diameter gets larger or smaller the smaller the sphere's surface area gets. right? so you can use alpha for the shere and the right and make the lengths equal each other like you said.