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Two astronauts, with masses of 55 kg and 84 kg, are initially at rest in outer space. They push each other apart. What is their separation after the lighter astronaut has moved 19 m?

Answer :

Final answer:

Using the conservation of momentum, we find that after the lighter astronaut moves 19 m, the heavier astronaut would move approximately 12.44 m in the opposite direction, resulting in a total separation of 31.44 m between them.

Explanation:

To determine the separation between two astronauts of masses 55 kg and 84 kg after they push each other apart in space, we can apply the principle of conservation of momentum. The total momentum of a system remains constant if there is no external force acting on the system. Since both astronauts are initially at rest, their total momentum is zero.

When the 55 kg astronaut moves 19 meters, the principle of conservation of momentum dictates that the 84 kg astronaut must move in the opposite direction. Since momentum ( P) is the product of mass and velocity, the momentum of the two astronauts must be equal and opposite. Let's say the 55 kg astronaut moves with a velocity V1 and covers 19 m, and the 84 kg astronaut moves with a velocity V2.

We have:

M1 * V1 = M2 * V2

where M1 is the mass of the lighter astronaut and M2 is the mass of the heavier astronaut.

The distance the heavier astronaut moves, let's call it D2, can be calculated as:

D1 / D2 = M2 / M1

So, D2 = (M1 / M2) * D1

Therefore:

D2 = (55 kg / 84 kg) * 19 m

D2 = 0.6548 * 19 m

D2 = 12.4412 m

So, the heavier astronaut will move approximately 12.44 meters in the opposite direction. As a result, the total separation between the two astronauts after the lighter astronaut has moved 19 m will be the sum of the distances each astronaut has moved relative to their initial position:

Total separation = 19 m + 12.44 m

Total separation = 31.44 m

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