How to Calculate Speed and Direction After Collision of Two Billiard Balls

The initial conditions of the two billiard balls before the head-on collision can be summarized as follows:

Mass of billiard ball A: 170 g

Mass of billiard ball B: 170 g

Initial velocity of billiard ball A: 8 m/s eastward

Initial velocity of billiard ball B: 2 m/s westward

When two billiard balls of equal mass collide head-on along the same line, the momentum of the system is conserved. This means that the total momentum before the collision is equal to the total momentum after the collision. To calculate the speed and direction of each ball after the collision, we can use the principle of conservation of momentum.

Step 1: Calculate the total momentum before the collision

Since the initial velocities of the balls are in opposite directions, we need to consider the direction as positive or negative. Let's take eastward as positive and westward as negative:

Total momentum before collision = (mass of A x velocity of A) + (mass of B x velocity of B)

Total momentum before collision = (0.17 kg x 8 m/s) + (0.17 kg x (-2 m/s))

Total momentum before collision = 1.36 kg m/s - 0.34 kg m/s

Total momentum before collision = 1.02 kg m/s

Step 2: Calculate the total momentum after the collision

Since the collision is elastic, the total momentum after the collision will also be 1.02 kg m/s as momentum is conserved in the absence of external forces.

Step 3: Calculate the speed and direction of each ball after the collision

Let the velocities of the balls after the collision be V_A and V_B. According to the conservation of momentum:

(mass of A x V_A) + (mass of B x V_B

(0.17 kg x V_A) + (0.17 kg x V_B

Given that V_A and V_B have opposite signs as they are moving in opposite directions, the speeds after the collision are:

Speed of ball A after collision = 1.02 kg m/s / 0.17 kg = 6 m/s eastward

Speed of ball B after collision = 1.02 kg m/s / 0.17 kg = 6 m/s westward

Therefore, after the head-on collision, billiard ball A will be moving eastward at 6 m/s and billiard ball B will be moving westward at 6 m/s.