Final answer:
The magnitude of the velocity of the larger ball after the collision can be calculated using the principle of conservation of linear momentum. It can be calculated to be approximately 1.477 m/s.
Step-by-step explanation:
The magnitude of the velocity of the larger ball after the collision can be calculated using the principle of conservation of linear momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision. In this case, we have a small ball with mass m = 0.270 kg moving at a speed of 3.00 m/s, and a larger ball with mass ma = 0.550 kg at rest. Let's assume the magnitude of the velocity of the larger ball after the collision is v2. The momentum of the small ball before the collision is given by m * v1, and the momentum of the larger ball after the collision is given by ma * v2. Therefore, applying the conservation of momentum, we have:
m * v1 = ma * v2
Substituting the given values, we get:
0.270 kg * 3.00 m/s = 0.550 kg * v2
Solving for v2, we find:
v2 = (0.270 kg * 3.00 m/s) / 0.550 kg
v2 ≈ 1.477 m/s
Therefore, the magnitude of the velocity of the larger ball after the collision is approximately 1.477 m/s.