Final answer:
The question is about the motion of a space probe breaking into three pieces and requires finding the velocity of the third piece. By using the law of conservation of momentum and solving an equation involving the masses and velocities, the velocity of the third piece can be determined.
Step-by-step explanation:
The given question involves the motion of a space probe as it breaks into three pieces. Let's refer to the first piece as m1 and the second piece as m2. According to the question, m1 has a mass of 42.8 kg and travels in the x-direction at a velocity of 12.0 m/s. On the other hand, m2 has a mass of 62.0 kg and travels in the xy-plane at an angle of 105 degrees.
To find the velocity of the third piece, we need to use the law of conservation of momentum. Since the space probe was initially at rest, the total momentum before the break is zero. Therefore, the total momentum after the break must also be zero. We can use this information to solve for the velocity of the third piece.
Let's denote the velocity of the third piece as v3. Using the formula for momentum (p = mv), we have the following equation:
m1vx1 + m2vx2 + m3vx3 = 0
Substituting the given values, we have:
(42.8 kg)(12.0 m/s) + (62.0 kg)(cos(105 degrees))(12.0 m/s) + m3v3 = 0
Solving for v3, we can determine the velocity of the third piece of the space probe.