# Conservation of Momentum of astronaut leaving ship

• TyroneTheDino
In summary, an astronaut is pushed from her ship at a velocity of 2m/s while carrying a 120kg tool belt. After 5 seconds, she decides to detach and throw the tool belt away from her at a velocity of 10m/s. Using the equations for conservation of momentum and distance, it can be determined that she will survive as she only travels 10m and has 240kg m/s of initial momentum. However, the question remains ambiguous as to whether the 10m/s velocity of the tool belt is relative to the astronaut or the initial reference frame. This would affect the outcome if the astronaut was pushed out at a speed of 10m/s instead of 2m/s.
TyroneTheDino

## Homework Statement

An astronaut is pushed from her ship at a velocity of 2m/s. Her weight including her tool belt is 120kg. Remembering Newtons 3rd law, she takes 5 seconds to decide to detach her belt and throw it away from her. The 20kg tool belt leaves her suit as she throws it in front of her 10m/s. If she has 20 minutes of air left in her tank, does she make it?

## Homework Equations

Conservation of Momentum
mvi=mvf

Distance
d=vt

## The Attempt at a Solution

I say that the astronaut survives.

Because of distance equation= (2)(5)=10m
Her initial momentum is 240kg m/s
And by throwing the belt in front of her she is propelled at -.4m/s
Since she only traveled 10m she would make it back on time.

I would start by revisiting conservation of momentum and assigning each of the velocity vectors a sign depending on whether they are directed towards the ship or away from the ship. I think that will really clear things up.

The question as stated seems to be a bit ambiguous to me. Is the speed that the tool belt is thrown meant to be taken relative to the astronaut or the initial reference frame? If she happened to be pushed out at a speed of 10 m/s instead of 2 m/s, would that mean she couldn't throw the tool belt away from herself at all?

gneill said:
The question as stated seems to be a bit ambiguous to me. Is the speed that the tool belt is thrown meant to be taken relative to the astronaut or the initial reference frame? If she happened to be pushed out at a speed of 10 m/s instead of 2 m/s, would that mean she couldn't throw the tool belt away from herself at all?
There are three reference frames to choose from for the 10m/s: the ship, the astronaut before throwing the belt, the astronaut after throwing the belt. For the question to be at least a bit interesting, I think it has to be the second.
Tyrone, how do you get the -.4m/s?

## 1. What is the Conservation of Momentum of an astronaut leaving a ship?

The Conservation of Momentum is a fundamental law of physics that states that the total momentum of a closed system remains constant in the absence of external forces. This means that when an astronaut leaves a ship in space, their momentum, which is the product of their mass and velocity, must be equal and opposite to the momentum of the ship in order for the total momentum of the system to remain constant.

## 2. Why is the Conservation of Momentum important for astronauts leaving a ship?

The Conservation of Momentum is important for astronauts leaving a ship because it ensures that their movement will not affect the overall motion of the ship. This is crucial in space where there is no external force to counteract any changes in momentum. It also allows for precise calculations and control of the spacecraft's movement.

## 3. What factors affect the Conservation of Momentum of an astronaut leaving a ship?

The Conservation of Momentum is affected by two main factors: the mass and velocity of the astronaut and the mass and velocity of the ship. The greater the mass or velocity of either the astronaut or the ship, the greater the momentum and therefore the greater the impact on the overall momentum of the system.

## 4. How does the Conservation of Momentum apply to space travel?

The Conservation of Momentum is a fundamental principle in space travel as it governs the movement of spacecrafts and astronauts in the absence of external forces. It allows for precise calculations and control of spacecrafts and ensures that their movements do not disrupt the overall motion of the system.

## 5. Can the Conservation of Momentum be violated?

The Conservation of Momentum is a fundamental law of physics and cannot be violated in a closed system. However, in open systems where external forces are present, the total momentum of the system can change. This is why astronauts must carefully plan and account for any external forces, such as gravity, when leaving a ship in space.

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