Final Speed of Billiard Ball A After Collision

What is the final speed of Billiard Ball A after the collision?

The final speed of Ball A after the collision is 6.8 m/s. According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. After the collision, Ball B is moving in the opposite direction with a velocity of 6.8 m/s. The final momentum of Ball B can be calculated as: Final momentum of Ball B = mass of Ball B * final velocity of Ball B = 3.9 kg * (-6.8 m/s) [since it is moving in the opposite direction] = -26.52 kg·m/s The final momentum of Ball A can be calculated using the conservation of momentum: Total initial momentum = Total final momentum (0 kg·m/s) + (68.25 kg·m/s) = (final momentum of Ball A) + (-26.52 kg·m/s) Simplifying the equation, we find: final momentum of Ball A = 26.52 kg·m/s To calculate the final velocity of Ball A, we divide the final momentum by the mass of Ball A: final velocity of Ball A = final momentum of Ball A / mass of Ball A = 26.52 kg·m/s / 3.9 kg = 6.8 m/s Therefore, the final speed of Ball A after the collision is 6.8 m/s.

Calculation of Final Speed of Ball A:

After the collision between Ball A (at rest) and Ball B (moving towards A), the final speed of Ball A can be determined using the conservation of momentum principle. The momentum of an object is the product of its mass and velocity. 1. Initial Momentum: Before the collision, the total initial momentum is calculated as: Total initial momentum = momentum of Ball A + momentum of Ball B = 0 kg·m/s + (3.9 kg * 17.5 m/s) = 68.25 kg·m/s 2. Final Momentum: After the collision, the total final momentum is equal to the total initial momentum: Total final momentum = final momentum of Ball A + final momentum of Ball B = 0 kg·m/s + (-26.52 kg·m/s) = 68.25 kg·m/s 3. Calculating Final Speed of Ball A: To find the final velocity of Ball A, we divide the final momentum (26.52 kg·m/s) by the mass of Ball A (3.9 kg): final velocity of Ball A = 26.52 kg·m/s / 3.9 kg = 6.8 m/s Therefore, the final speed of Billiard Ball A after the collision is 6.8 m/s.
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