Two dimensional perfectly elastic collision of billiard balls, physics. Momentum in two dimensions.

Perfectly elastic two dimensional collision between billiard balls. 🧠 Access full flipped physics courses with video lectures and examples at https://www.zakslabphysics.com/ In this conservation of momentum two dimensions billiard ball perfectly elastic collision, we compute the final speeds and one of the directions for a collision between two billiard balls in which the final direction of one of the balls is given. Conservation of momentum for momentum components in two dimensions in the x and y directions and conservation of energy give us a system of two 2D elastic collision equations and two unknowns. The system requires a trig identity trick, using (sin(x))^2 + (cos(x))^2 =1 to eliminate theta before solving the remaining non-linear system using substitution. In the two dimensional billiard ball elastic collision, we have four variables for the final state: the angles and speeds of the two balls. Thus, for an elastic collision of pool balls physics problem, one of these variables must be given in order to solve the problem with our three equations: x momentum, y momentum, and kinetic energy. This makes sense, because the angle the balls bounce off each other depends on how directly they collide, giving us a degree of freedom in the 2D perfectly elastic collision of billiard balls momentum in two dimensions analysis.