Final answer:
The question asks for the direction of the velocity of the third part of a 34.0-kg object that breaks into three pieces post-explosion, using conservation of momentum. By analyzing the momentum conservation in both the east-west and north-south directions, we can determine the third part's direction of motion.
Step-by-step explanation:
The question involves an application of conservation of momentum, where an object explodes into three parts and we have to find the direction of the velocity of the third part. Since momentum is a vector quantity, we consider the momentum in the north-south and east-west directions separately. When the 34.0-kg object explodes, we'll have the momentum conserved in both directions.
For the east-west direction (x-axis), we have the momentum of part 1 (5.40 kg × 54.0 m/s), and for the north-south direction (y-axis), we have the momentum of part 2 (5.80 kg × 81.0 m/s) and part of the initial momentum of the object (34.0 kg × 29.0 m/s). The unknown is the momentum of part 3 which can be resolved into two components: one along the east-west direction and the other along the north-south direction. Using the given masses and velocities, we calculate the missing component and thus find the direction of the third part's velocity, which is the direction this third fragment travels relative to due west (north of west).