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------------------------------------------------ Two chunks of space debris collide in space. The smaller chunk was moving forward and hit a larger piece of debris that was initially stationary relative to the reference point (the International Space Station).

- Piece one of debris has a mass of 2.67 kg.
- The other chunk has a mass of 5.83 kg.

After the collision:
- The 2.67 kg chunk diverts upward at an angle of 28 degrees with a velocity of 185 m/s.
- The 5.83 kg chunk moves forward with a velocity of 172 m/s.

Question:
What is the initial velocity of chunk one and the angle for the final velocity of chunk two?

The initial velocity of chunk one is zero and the angle for the final velocity of chunk two can be found by solving the equation v2 * sin(θ) = 185 * sin(28°).

Explanation:

To find the initial velocity of chunk one and the angle for the final velocity of chunk two, we can use the principles of conservation of momentum and the laws of motion.

Let's denote the initial velocity of chunk one as v1 and the angle for the final velocity of chunk two as θ.

According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.

Before the collision:

The momentum of chunk one is given by m1 * v1, where m1 is the mass of chunk one.
The momentum of chunk two is zero since it is considered stationary.

After the collision:

The momentum of chunk one is given by m1 * v1.
The momentum of chunk two is given by m2 * v2, where m2 is the mass of chunk two and v2 is the final velocity of chunk two.

Using the given information, we can set up the following equations:

Before the collision: m1 * v1 = 0

After the collision: m1 * v1 = m2 * v2

From the first equation, we can conclude that the initial velocity of chunk one, v1, is zero.

Substituting this value into the second equation, we can solve for the final velocity of chunk two, v2.

Finally, to find the angle for the final velocity of chunk two, θ, we can use trigonometry. We know that the vertical component of the final velocity is given by v2 * sin(θ). Since the smaller chunk diverts upward at an angle of 28 degrees, we can set up the equation:

v2 * sin(θ) = 185 * sin(28°)

Solving this equation will give us the value of θ.

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