Each croquet ball in a set has a mass of 0.45

kg. The green ball, traveling at 12.6 m/s,
strikes the blue ball, which is at rest.
Assuming that the balls slide on a friction-
less surface and all collisions are head-on, find
the final speed of the blue ball in each of the
following situations:
a) The green ball stops moving after it
strikes the blue ball.
Answer in units of m/s.

To find the final speed of the blue ball in this situation, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object is defined as the product of its mass and velocity. In this case, the momentum of a ball is given by the equation:

Momentum = mass × velocity

Let's denote the mass of the green ball as m1 (0.45 kg) and the mass of the blue ball as m2 (also 0.45 kg). The initial velocity of the green ball is v1 (12.6 m/s), and the initial velocity of the blue ball is v2 (0 m/s since it is at rest). The final velocity of the green ball after the collision is v1' (0 m/s), and we need to find the final velocity of the blue ball after the collision, v2'.

According to the conservation of momentum:

m1 × v1 + m2 × v2 = m1 × v1' + m2 × v2'

Since the green ball stops moving after the collision (v1' = 0 m/s), the equation simplifies to:

m1 × v1 = m2 × v2'

Plugging in the given values:

(0.45 kg) × (12.6 m/s) = (0.45 kg) × v2'

Simplifying the equation:

5.67 = 0.45 × v2'

To isolate v2', we divide both sides of the equation by 0.45:

v2' = 5.67 / 0.45

Calculating the value:

v2' ≈ 12.6 m/s

Therefore, the final velocity of the blue ball after the collision is approximately 12.6 m/s.