Astronaut Problem: Homework Equations and Solution Attempt

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In summary: So I get about 1684 m/s too.In summary, the question asks for the muzzle speed of a bullet fired horizontally on the Moon in order to complete a full orbit and return to its original location. Using the equation for centripetal acceleration and the given information about the Moon's gravity and radius, a muzzle speed of approximately 1684 m/s is calculated.
  • #1
blackboy
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Homework Statement


An astronaut standing on the Moon fires a gun so that the bullet leaves the barrel moving in a horizontal direction. What must be the muzzle speed of the bullet so that it travels completely around the Moon and return to its original location? How long does this trip take? Assume that the the free fall acceleration on the Moon is one-sixth that on Earth.


Homework Equations





The Attempt at a Solution


Say the height of the guy is y. I got the circumference as 1092100m. So vt=1092100. t also satisfies y=(gt^2)/12. Then I get y=(9.74*10^11)/(v^2). I don't know where else to go with this.
 
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  • #2
Basically the bullet needs to go into orbit at the radius of the surface doesn't it?

So centripetal acceleration needs to match moon gravity.

m*v2/r = m*gmoon = m*g/6

v = (r*g/6)1/2
 
  • #3
No but this is in motion in 2d. I don't want to bring m into it yet. Is there a way to do it with pure 2d Motion stuff.
 
  • #4
But m is canceled out. Do you mean that you don't want to use a=v^2/r ??
 
  • #5
blackboy said:
No but this is in motion in 2d. I don't want to bring m into it yet. Is there a way to do it with pure 2d Motion stuff.

When the centripetal acceleration outward is the same as gravity inward ... shouldn't it go on and on, unless it hits a crater wall taller than where the astronaut is standing?

Why do you think it is not in 2D motion?
 
  • #6
Oh I overreacted when I saw the m. I know it was 2d motion, but I didn't want to use m or any dynamic stuff yet.
 
  • #7
I had a few errors in the first post. Anyway I got y=1.23 and v=2838733. Thanks
 
  • #8
blackboy said:
I had a few errors in the first post. Anyway I got y=1.23 and v=2838733. Thanks

I hope you are missing a decimal point. That's speed of light territory.
 
  • #9
Ok yea dum error. v=1684?
 
  • #10
blackboy said:
1.So vt=1092100. t also satisfies y=(gt^2)/12. Then I get y=(9.74*10^11)/(v^2).


You have a bullet in a circular orbit, so what does "y" represent? The equation y=(1/2)at^2 only applies if the acceleration is of constant magnitude and constant direction. In this case, the direction of the acceleration constantly changes to point to the Moon's center, so you can't use that equation.
 
  • #11
blackboy said:
Ok yea dum error. v=1684?

Close enough I suppose. I get 1660 m/s scratching it out roughly.
 
  • #12
LowlyPion, what do you mean when you say "the centripital acceleration outward"? There is only one force on the bullet. Here's what I got.

[tex] mv^2/r = GmM/r^2 v = sqrt(GM/r) = sqrt(1/6gr) [/tex]

Plugging in values I get 532 m/s.
 
Last edited:
  • #13
nealh149 said:
LowlyPion, what do you mean when you say "the centripital acceleration outward"? There is only one force on the bullet. Here's what I got.

[tex] mv^2/r = GmM/r^2 v = sqrt(GM/r) = sqrt(1/6gr) [/tex]

Plugging in values I get 532 m/s.

That's because you are assuming that the circumference the questioner gave, 1092100 m, is right. It's not; it corresponds to a radius of 173.8 km whereas the actual radius is 1738 km, one decimal place off. 1684 m/s is right if 1738 km is used.
 
  • #14
Okay, that's true, I did assume the OP's circumference was correct.
 

1. What is the "Astronaut Problem"?

The "Astronaut Problem" is a mathematical problem that involves finding the distance traveled by an astronaut who is moving in a straight line at a constant speed, while also taking into account the effects of gravity and air resistance.

2. What are the homework equations for the "Astronaut Problem"?

The homework equations for the "Astronaut Problem" are the equations of motion, specifically the equation for distance traveled (d = v0t + 1/2at^2) and the equation for velocity (v = v0 + at), where v0 is the initial velocity, a is the acceleration, and t is the time.

3. How do you solve the "Astronaut Problem"?

To solve the "Astronaut Problem", you first need to use the homework equations to set up a system of equations with the given information. Then, you can solve for the unknown variables using algebraic manipulations. Finally, plug in the values to find the distance traveled by the astronaut.

4. What are some common mistakes when attempting to solve the "Astronaut Problem"?

Some common mistakes when attempting to solve the "Astronaut Problem" include not setting up the equations correctly, using the wrong units for the given values, and not considering the effects of air resistance on the astronaut's motion.

5. How can the "Astronaut Problem" be applied in real life?

The "Astronaut Problem" can be applied in real life situations where an object is moving in a straight line with constant speed, while also experiencing the effects of gravity and air resistance. This can include calculating the distance traveled by a skydiver or a bullet fired from a gun.

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