# An astronaut who strays too for from her ship could use a pistol to get back by firing in the opposite direction. Make some reasonable assumption about the astronaut's mass and the mass and speed...

An astronaut who strays too for from her ship could use a pistol to get back by firing in the opposite direction. Make some reasonable assumption about the astronaut's mass and the mass and speed of the bullet to see how fast a single shot would make the astronaut go.

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### 1 Answer

There are several ways of solving a problem like this, such as using potential and kinetic energy equations instead of the usual kinematic equations. Unfortunately, since we have no actual data to work with, most of the answer is going to be conjectural.

What we can do is find sources for a reasonable human mass, and a reasonable mass and velocity of a pistol bullet, and then apply this information to the most relevant kinematic equations. Since we have no existing data for how quickly the astronaut is moving away from her spaceship, we can simply set her velocity to zero, and then determine the velocity that would be imparted on her by the force of the bullet firing.

An average human is about 65kg.

An average pistol bullet is about 5g, or .005kg. A reasonable speed is 300m/s, and a reasonable barrel length is .1m

A good equation to use here is Vf^2 = Vi^2 + 2ad

300^2 = 0^2 + 2 a .1

Rearranging to solve for a: (300^2) / .2 = a

a = 450,000

F=ma, so F = .005 (450,000) = 2250N

If the 65kg astronaut is subjected to a 2250N force, then the subsequent acceleration should be 2250/65 = 34.6m/s

We can use Vf = Vi + at to determine the time it takes the bullet to fire, and therefore the time the astronaut is subjected to the 2250N force.

300 = 0 + 450000(t)

t = 300/450000 = 6.66x10^-4

Vf = Vi + at

Vf = 0 + (34.6)(6.66x10^-4) = .023m/s

This also makes sense in terms of proportions: the 65kg astronaut is 13,000 times more massive than the .005kg bullet, so the same force over the same time should produce an effect 13,000 times smaller.

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