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 (√3R/2,R/2).

Reference Problem:
Two identical billiard balls collide. The first one is initially traveling at (2.2m/s)ˆi−(0.4m/s)ˆj and the second one at −(1.4m/s)ˆi+(2.4m/s)ˆj. 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: (-0.48m/s)ˆi+(1.92m/s)ˆj, Ball 2: (-1.28m/s)ˆi+(0.48m/s)ˆj
b) Ball 1: (-1.28m/s)ˆi+(0.48m/s)ˆj, Ball 2: (-0.48m/s)ˆi+(1.92m/s)ˆj
c) Ball 1: (-0.48m/s)ˆi+(1.92m/s)ˆj, Ball 2: (1.28m/s)ˆi+(0.48m/s)ˆj
d) Ball 1: (1.28m/s)ˆi+(0.48m/s)ˆj, Ball 2: (-0.48m/s)ˆi+(1.92m/s)ˆj

Answer 1

To solve this problem, we can use the principle of conservation of momentum. By applying the conservation of momentum and solving the equation, we can determine the final velocities of the balls.

Step-by-step explanation:

To solve this problem, we can use the principle of conservation of momentum. When two balls collide, the total momentum before the collision is equal to the total momentum after the collision.

Let's denote the initial velocities of the two balls as v1 and v2, and the final velocities as v'1 and v'2. Applying the conservation of momentum, we have:

m1v1 + m2v2 = m1v'1 + m2v'2

For this problem, the initial velocities of the balls and their masses are given. By substituting these values into the equation and solving for the final velocities, we can determine the answer which is Ball 1: (-0.48m/s)î + (1.92m/s)ĵ and Ball 2: (-1.28m/s)î + (0.48m/s)ĵ.