During practice, a student kicks a 0.43 kg soccer ball with a velocity of 8.4 m/s into a 0.15 kg bucket. What is the final velocity of the combined mass if the bucket travels with the ball after the collision.
When the student kicks the soccer ball into the bucket the bucket and the ball travel together. This is the case when there is an inelastic collision between the two.
The total momentum of a system in conserved in an inelastic collision. Initially only the ball is in motion. The mass of the ball is 0.43 kg and it is traveling at 8.4 m/s. As the bucket is still, the total momentum of the system is 0.43*8.4 = 3.612 kg*m/s
After collision, the bucket weighing 0.15 kg and the ball travel at the same velocity. Let this be equal to V.
The total momentum after collision is 0.43*V + 0.15*V = 0.58*V. As this should be equal to the total initial momentum
0.58*V = 3.612
V = 3.612/0.58
=> V = 6.23 m/s
The final velocity of the combined mass is 6.23 m/s