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.

in simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g. this is also known as upthrust.