Two chunks of space debris collide head-on in an elastic collision. One piece of debris has a mass of 2.67 kg, and the other chunk has a mass of 5.83 kg. After the collision, both chunks move in the direction of the second chunk's initial velocity with speeds of 185 m/s for the smaller chunk and 172 m/s for the larger chunk.

What are the initial velocities of the two chunks?

In an elastic collision, both momentum and kinetic energy are conserved. To solve this problem, we'll use the principles of conservation of momentum and kinetic energy.

Write down the given information:

Mass of first chunk (m1) = 2.67 kg

Mass of second chunk (m2) = 5.83 kg

Velocity of first chunk after collision (v1') = 185 m/s

Velocity of second chunk after collision (v2') = 172 m/s

Apply conservation of momentum:

Before collision:

Total momentum = m1 * v1 + m2 * v2

After collision:

Total momentum = m1 * v1' + m2 * v2'

Using the given values:

m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2'

Substitute the given values:

(2.67 kg) * v1 + (5.83 kg) * 0 = (2.67 kg) * 185 m/s + (5.83 kg) * 172 m/s

Solve for v1:

v1 = [(2.67 * 185) + (5.83 * 172)] / 2.67

Calculate v1:

v1 = 312.046 m/s

Calculate v2 using the conservation of momentum:

v2 = (m1 * v1 + m2 * v2' - m1 * v1') / m2

Substitute the known values:

v2 = (2.67 * 312.046 + 5.83 * 172 - 2.67 * 185) / 5.83

Calculate v2:

v2 = 77.954 m/s

So, the initial velocities of the two chunks are 312.046 m/s and 77.954 m/s respectively.