Final answer:
The initial momentum of the system is 43 kg.m/s. The velocity of the 5 kg ball after the collision is -6 m/s.
Step-by-step explanation:
The initial momentum of the system can be calculated by adding the momentum of the 7 kg bowling ball and the momentum of the 5 kg bowling ball. Momentum is defined as the product of an object's mass and its velocity. So, the initial momentum of the system is (7 kg * 11 m/s) + (5 kg * -9 m/s) = 43 kg.m/s.
After the collision, the 7 kg bowling ball bounces back with a velocity of 7 m/s. To find the velocity of the 5 kg ball, 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. Since the only objects involved in the collision are the 7 kg and 5 kg bowling balls, the final momentum of the system is (7 kg * -7 m/s) + (5 kg * v), where v is the velocity of the 5 kg ball after the collision. Equating the initial and final momentum, we get 43 kg.m/s = -49 kg.m/s + 5 kg * v. Solving this equation for v, we find that the velocity of the 5 kg ball after the collision is -6 m/s.