Question

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?

a) Ball 1: (-1.28m/s)^i+(0.48m/s)ʲ, Ball 2: (1.92m/s)^i+(1.92m/s)ʲ
b) Ball 1: (0.48m/s)^i+(1.92m/s)ʲ, Ball 2: (-1.28m/s)^i+(0.48m/s)ʲ
c) Ball 1: (-1.28m/s)^i+(0.48m/s)ʲ, Ball 2: (-1.92m/s)^i+(1.92m/s)ʲ
d) Ball 1: (0.48m/s)^i+(1.92m/s)ʲ, Ball 2: (1.28m/s)^i+(0.48m/s)ʲ

Answer 1

The final velocities of the two identical billiard balls can be calculated using the principles of conservation of momentum and conservation of kinetic energy. The correct answer is Ball 1: (-1.28 m/s)^i + (0.48 m/s)^j, Ball 2: (1.92 m/s)^i + (1.92 m/s)^j

Step-by-step explanation:

The final velocities of two identical billiard balls can be calculated using the principles of conservation of momentum and conservation of kinetic energy. When two objects collide, the total momentum before the collision is equal to the total momentum after the collision, and the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

In this case, the initial velocities of the two billiard balls are given. To find the final velocities, we can use the following formulas:

V1,f = (m1-m2)v1,i + 2m2v2,i / (m1+m2)

V2,f = 2m1v1,i + (m2-m1)v2,i / (m1+m2)

Using the given initial velocities and the fact that the billiard balls are identical, we can substitute the values into these formulas and calculate the final velocities. The correct answer is:

Ball 1: (-1.28 m/s)^i + (0.48 m/s)^j, Ball 2: (1.92 m/s)^i + (1.92 m/s)^j