Could some explain this question to me in detail? it is extremely vital for me to understand this question. in advance!

question is in the image

v₁ = 0.45 m/s or v₂ = -0.10 m/s

Explanation:

Marble 1 has a mass of m and an initial velocity of -0.30 m/s.

Marble 2 has a mass of m/2 and an initial velocity of 0.80 m/s.

Momentum is conserved, so:

m (-0.30) + m/2 (0.80) = m v₁ + m/2 v₂

-0.3m + 0.4m = m v₁ + m/2 v₂

0.1m = m v₁ + m/2 v₂

0.1 = v₁ + 1/2 v₂

One of the marbles has half the speed after the collision.  Let's first assume that it's Marble 1.  That means v₁ = -0.15 m/s or 0.15 m/s.

If v₁ = -0.15 m/s:

0.1 = -0.15 + 1/2 v₂

0.25 = 1/2 v₂

0.5 = v₂

This isn't possible; at least one of the marbles must change direction.

If v₁ = 0.15 m/s:

0.1 = 0.15 + 1/2 v₂

-0.05 = 1/2 v₂

-0.1 = v₂

This is a possible solution.

Now, let's assume that Marble 2 is the one that moves at half the speed.  That means v₂ = -0.40 m/s or 0.40 m/s.

If v₂ = -0.40 m/s:

0.1 = v₁ + 1/2 (-0.40)

0.25 = v₁ − 0.2

0.45 = v₁

This is a possible solution.

If v₂ = 0.40 m/s:

0.1 = v₁ + 1/2 (0.40)

0.1 = v₁ + 0.2

-0.1 = v₁

This isn't possible; at least one of the marbles must change direction.

Therefore, there are two possible answers: v₁ = 0.45 m/s, or v₂ = -0.10 m/s.

the skeletons of most mammals reach a certain size and then stop growing. however, many animals, including some mammals, keep growing throughout their lives. kangaroos, for example, just keep growing and growing until they die. also, the longer an animal lives the greater the chance it might catch some deadly disease.