Final answer:
The speed of the boat immediately after the child throws the package is 0.6812 m/s in the opposite direction to the throw, based on the conservation of momentum.
Step-by-step explanation:
The question revolves around the conservation of momentum principle in physics. When a child in a motionless boat throws a package, the child and the boat will move in the opposite direction to conserve momentum. To find the speed of the boat immediately after, we use the conservation of momentum equation: (mass of child and boat) × (final velocity of child and boat) = (mass of package) × (velocity of package). Since the boat is initially at rest, its initial momentum is zero.
Let's denote the speed of the boat after the package is thrown as V. The equation becomes:
(69.0 kg × V) = (4.70 kg × 10.0 m/s),
which simplifies to:
V = (4.70 kg × 10.0 m/s) / 69.0 kg.
Calculating this gives us the final velocity of the boat.
So, V = 47.0 kg·m/s / 69.0 kg = 0.6812 m/s.
The boat's speed immediately after the package is thrown is 0.6812 m/s in the opposite direction of the throw.