Final answer:
The combined velocity of the soccer ball and bucket after the collision, calculated using the conservation of momentum for an inelastic collision, is 6.18 m/s.
Step-by-step explanation:
To find the velocity of the bucket and ball after the collision, we apply the principle of conservation of momentum because no external forces are acting on the bucket-ball system. In an inelastic collision, the objects stick together after the collision, and the total momentum before the collision is equal to the total momentum after the collision.
The momentum of the soccer ball before the collision can be calculated using the formula: momentum = mass × velocity. Thus, the momentum of the soccer ball is:
0.40 kg × 8.5 m/s = 3.4 kg·m/s
Because the bucket is initially at rest, its initial momentum is 0 kg·m/s. The total momentum of the system before the collision is:
3.4 kg·m/s + 0 kg·m/s = 3.4 kg·m/s
After the collision, the total mass of the bucket and ball is 0.40 kg + 0.15 kg = 0.55 kg. Since momentum is conserved, the final combined mass and velocity (v) will also have a momentum of 3.4 kg·m/s:
0.55 kg × v = 3.4 kg·m/s
Solving for v, we find:
v = 3.4 kg·m/s / 0.55 kg = 6.18 m/s
Therefore, the combined velocity of the soccer ball and bucket after the collision is 6.18 m/s.