Final answer:
In a physics problem applying conservation of momentum, a 68 kg skater throws a 10 kg snowball resulting in a recoil motion. The skater's velocity is calculated to be (-7.794i - 2.059j) m/s, indicating motion in the opposite direction of the snowball with a proportionally smaller magnitude.
Step-by-step explanation:
Physics Concept Application
The student's question involves the application of the principle of conservation of momentum, which is a fundamental concept in physics. Specifically, this question is asking about the scenario where a 68 kg skater on frictionless ice throws a 10 kg snowball with a given velocity vector (v=53.0i+14.0j m/s).
To solve this problem, we first recognize that due to Newton's third law, the skater will experience a change in momentum equal in magnitude and opposite in direction to the momentum given to the snowball. The initial momentum of the skater is zero since they start at rest. After throwing the snowball, the skater will have a momentum equal to the negative of the snowball's momentum.
The skater's velocity vector after throwing the snowball is (-7.794i - 2.059j) m/s. This indicates that the skater moves in the opposite direction to the snowball's motion with a smaller magnitude due to the skater's larger mass.