Final answer:
To find the velocity direction of part (3) after an explosion, we apply the conservation of momentum, considering the momentum components along the north-south and east-west directions and using vector analysis.
Step-by-step explanation:
The question asks us to determine the direction of the velocity of part (3) after a 31.0-kg object, initially moving due north, explodes into three parts. Conservation of momentum must be used to solve the problem because momentum is conserved in an isolated system such as an explosion without external forces. The momentum before the explosion in the north-south and east-west directions must equal the momentum after the explosion in those respective directions.
To find the velocity of part (3), we use the fact that the total momentum before the explosion is equal to the combined momentum of all three parts after the explosion. Since the initial momentum was only in the north direction (as no information about east or west movement was provided), we assume there was no initial east-west momentum. Therefore, after the explosion, the east-west momentum of parts (1) and (3) should cancel each other out, as should the north-south momentum of parts (2) and (3).
Using the given masses and velocities of parts (1) and (2), we can calculate the momentum of part (3) by subtracting the momenta of parts (1) and (2) from the initial momentum of the object. The direction of the velocity of part (3) is then found using vector analysis of its momentum components.