Final answer:
To solve for the velocity of the third mass, we must use conservation of momentum, but the question does not provide all necessary values to calculate the exact velocity. The third mass would move in a direction that balances the momentum of the other two, which indicates it would be in the northwest direction.
Step-by-step explanation:
The question revolves around the principles of conservation of momentum. Since the object after explosion splits into three equal masses and two are given specific directions and velocities, the third mass's velocity can be determined using vector addition. The momentum of the system must be conserved; therefore, the total vector momentum after the explosion should be zero if the system was initially at rest. Using vector components, we can calculate the resulting vector of the third mass, which must balance out the vectors of the given two masses.
For the first object going east at 15.0 m/s, that's a vector purely in the positive x-direction. The second mass at 10.0 m/s at 45o S of E has both x and y components. To balance these, the third mass must have a velocity vector that, when added to the other two, yields a zero vector sum. This would be in the northwest direction, to cancel both the eastern and southern components.
However, as the exact values of the mass and velocity of the third object were not provided, we cannot give the exact answer without making assumptions. It's also worth noting that the provided SEO examples are related to different physics concepts and examples but do not directly relate to solving the original question.