Final answer:
The magnitude of the momentum of the 70 kg object, which was initially at rest, is 250 kg·m/s, having an equal magnitude and the opposite direction of the first object to conserve total momentum.
Step-by-step explanation:
When two objects push apart from each other, they obey the principle of conservation of momentum. This principle states that the total momentum of an isolated system remains constant if no external forces act on it. If an object with a mass of 50 kg is moving at 5 m/s, its momentum is calculated as the product of mass and velocity, which equals 250 kg·m/s (50 kg * 5 m/s).
Since the system started at rest and no external forces are present, the momentum of the second object, with a mass of 70 kg, must have an equal magnitude but opposite direction, to conserve the total momentum of the system. Thus, the magnitude of the momentum of the second object is also 250 kg·m/s.