Final answer:
Using the conservation of momentum principle in Physics, the speed of the second child after pushing off would be 4 m/s in the opposite direction of the first child's motion because their initial total momentum was zero.
Step-by-step explanation:
The question involves the conservation of momentum, which is a principle of Physics. When two children on ice skates push off from each other, the total momentum before and after the event is conserved because they are considered an isolated system (ignoring external forces such as friction because they are on ice). Assuming they start from rest, their initial total momentum is zero.
Therefore, after pushing off, if the first child with a mass of 30 kg moves away at a speed of 2 m/s, the second child with a mass of 15 kg must move in the opposite direction with a momentum that makes the total momentum remain zero. Since momentum is the product of mass and velocity (p = m * v), we can set up the equation:
Mass of first child (30 kg) * Velocity of first child (2 m/s) + Mass of second child (15 kg) * Velocity of second child (v) = 0.
Solving for the velocity of the second child (v), we get: v = - (30 kg * 2 m/s) / 15 kg = -4 m/s. The negative sign indicates that the direction of the second child is opposite to that of the first child's initial direction. Therefore, the correct answer is B) 4 m/s.