Velocity After Collision Calculation

What is the velocity of the red ball after the collision?

Given that the blue ball strikes the stationary red ball, what is the velocity of the red ball after the collision?

The velocity of the red ball after the collision is 2 m/s

When a blue 0.25 kg billiard ball, rolling at 2 m/s, strikes a stationary red 0.25 kg billiard ball, the red ball rolls off in the same direction that the blue ball was rolling. The blue ball comes to a stop after the collision. To calculate the velocity of the red ball after the collision, we can use the conservation of momentum principle.

First, we analyze the question to obtain useful information:

  • Mass of blue billiard ball (m₁) = 0.25 kg
  • Initial velocity of blue billiard ball (u₁) = 2 m/s
  • Mass of red billiard ball (m₂) = 0.25 kg
  • Initial velocity of red billiard ball (u₂) = 0 m/s
  • Velocity of blue billiard ball after collision (v₁) = 0 m/s
  • Velocity of red billiard ball after collision (v₂) = ?

Next, we calculate the velocity of the red billiard ball after collision:

Using the momentum conservation formula:

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Substitute the values:

(0.25 * 2) + (0.25 * 0) = (0.25 * 0) + (0.25 * v₂)

0.5 + 0 = 0 + 0.25v₂

0.5 = 0.25v₂

v₂ = 0.5 / 0.25 = 2 m/s

Therefore, the velocity of the red billiard ball after collision is 2 m/s.

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