Question

Repeat the preceding problem if the balls collide when the center of ball 1 is at the origin and the center of ball 2 is at the point (0,2R).

Reference Problem:
Two identical billiard balls collide. The first one is initially traveling at (2.2m/s)^i−(0.4m/s)ʲ and the second one at −(1.4m/s)^i+(2.4m/s)ʲ. Suppose they collide when the center of ball 1 is at the origin and the center of ball 2 is at the point (2R,0) where R is the radius of the balls. What is the final velocity of each ball?

Answer 1

To solve the problem of two billiard balls colliding at specific points, principles of conservation of momentum and kinetic energy are applied, leading to a system of equations used to find the final velocities.

Step-by-step explanation:

To determine the final velocities of the two billiard balls that collide at the points given, namely when the center of ball 1 is at the origin and the center of ball 2 is at the point (0, 2R), we must assume an elastic collision and use the principles of conservation of momentum and conservation of kinetic energy. Assuming the collision is two-dimensional, we use the following steps:

• Conservation of momentum along the x-axis and y-axis separately.
• Conservation of kinetic energy since the collision is elastic.
• System of equations from conservation laws to solve for the final velocities of each ball.

Given the different collision point compared to the problem at (2R, 0), the direction of momentum exchange will be different, which would lead to different final velocities that must be calculated using the collision's specific geometry.