A 2.2 kg rat floating in space pushes a piece of cheese away from himself at 10 m/s. The cheese has a mass of 1.1 kg. What is the velocity of the rat after he pushes the piece of cheese? 20 m/s
5 m/s
10 m/s
The rat doesn't move

The velocity of the rat after he pushes the cheese is 5 m/s

Explanation:

The question relates to the Law of conservation of linear momentum, which states that the total momentum in an isolated system is constant

The given parameters are;

The mass of the rat, floating, m₁ = 2.2 kg

The velocity with which the rat pushes the cheese away from himself, v₃ = 10 m/s = The final velocity of the cheese

The mass of the cheese, m₂ = 1.1 kg

Assuming that the initial velocity of the rat, v₁ = The initial velocity of the rat, v₂ = 0 m/s

Let, 'v₄', represent the velocity of the rat after he pushes the cheese, by the law of conservation of linear momentum we have;

The total initial momentum = The total final momentum

The total initial momentum = m₁·v₁ + m₂×v₂ = 2.2 kg × 0 m/s + 1.1 kg × 0 m/s = 0 kg·m/s

The total initial momentum = 0 kg·m/s

The total final momentum = m₁·v₄ + m₂×v₃ = 2.2 kg × v₄ + 1.1 kg × 10 m/s = 2.2·v₄ kg·m/s + 11 kg·m/s

The total final momentum = 2.2·v₄ kg·m/s + 11 kg·m/s

By the equality of the total initial momentum and the total final momentum, we have;

0 kg·m/s = 0 = 2.2·v₄ kg·m/s + 11 kg·m/s

2.2·v₄ kg·m/s + 11 kg·m/s = 0

2.2·v₄ kg·m/s = -11 kg·m/s

v₄ = -11 kg·m/s/(2.2 kg·m/s) = 5 m/s

The velocity of the rat after he pushes the cheese = v₄ = 5 m/s.

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