Final answer:
The final speed of the child and wagon is approximately 2.8696 m/s.
Step-by-step explanation:
To find the final speed of the child and wagon, we can use the principle of conservation of momentum. The initial momentum of the system is equal to the final momentum of the system. Since the ball is dropped vertically and there is no horizontal force acting on the system, the horizontal momentum remains constant.
Before the ball is dropped, the child and wagon have a combined momentum of 20 kg * 3.3 m/s = 66 kg·m/s (taking positive direction as forward). After the ball is dropped, the child and wagon still have the same momentum, but now with a combined mass of 23 kg (20 kg child + 1 kg ball + 2 kg wagon). Therefore, the final speed of the child and wagon is 66 kg·m/s divided by 23 kg, which is approximately 2.8696 m/s.