Final answer:
The question requires applying conservation of momentum principles to find the unknown velocity of a piece of an object that has broken into two parts. By equating the initial momentum with the momentums of the two pieces post-breakup and solving the system of equations, the velocity of the second piece can be determined.
Step-by-step explanation:
The question involves finding the velocity of the second piece of an object that breaks apart, using the principles of momentum conservation. In physics, whenever objects interact, the total momentum before the interaction is equal to the total momentum after, provided no external forces act on the system. For the provided scenario, we will assume a perfectly inelastic collision where the object has broken into two pieces.
To solve this, first, we determine the initial momentum of the object before it broke into two pieces using the mass and velocity given. After the break, the momentum of the 4.8-kg piece can be calculated with its mass and the given velocity post-breakup. By conserving momentum, we can set the initial momentum equal to the sum of the momentums of the two pieces, and solve for the unknown velocity of the second piece.
The calculation would go as follows:
Initial momentum = mass × initial velocity = 8 kg × 15 m/s × cos(32°)i - 8 kg × 15 m/s × sin(32°)j
Momentum of 4.8-kg piece = 4.8 kg × 12 m/s × (-j)
The momentum of the second piece will have both i and j components, and by creating a system of equations using the conservation of momentum principle (initial momentum = sum of momentums after), the velocity of the second piece can be found.