The final speed of the child and wagon increases after the 1.5 kg ball is dropped due to the conservation of momentum, with the new speed being slightly higher than the initial velocity.
The question involves the conservation of momentum, which is a principle of physics applied to a situation where a child drops a ball from a wagon. We start with the initial combined momentum of the child and wagon and set it equal to the final momentum of the child, wagon, and ball (separate entities now) after the ball has been dropped. The system's initial momentum is the mass of the child and wagon multiplied by their initial velocity. The final momentum is the sum of the momenta of the child (plus wagon) and the ball, which can be calculated separately and then combined.
Using the formula for momentum (p = mv), the initial momentum is (23 kg + 3.0 kg) × 2.2 m/s. After dropping the ball, the mass of the child and the wagon system is reduced to 23 kg. To find the final velocity of the child and wagon, we set up the equation preserving total momentum since no external forces are acting on the horizontal direction.
Initial momentum = Final momentum of child and wagon + Final momentum of the ball. Since the ball is dropped, its final momentum is zero. The conservation of momentum equation simplifies to (26 kg × 2.2 m/s) = (23 kg × final velocity). Solving for the final velocity gives us a value slightly higher than the initial velocity since the total mass of the moving system is now reduced. The final speed can be found by dividing the initial momentum by the new mass of the child and wagon.
So, dropping the ball leads to an increase in the velocity of the child and wagon due to the conservation of momentum.