How far apart are the astronaut and satellite after 8.67 minutes?

[alexi_b]

Homework Statement

A 63.8kg spacewalking astronaut pushes off a 678.0kg satellite, exerting a 156.0N force for the 0.870s it takes him to straighten his arms. How far apart are the astronaut and the satellite after 8.67min?

Homework Equations

The Attempt at a Solution

I tried just finding the acceleration of the satellite using Fnet=ma and then using that acceleration to place it into d=1/2at^2 (assuming the satellite was at rest) The answer came up into the thousands so I knew I did something wrong. I have no idea of how to start this question so it'd be great if someone could help out!

Thanks!

 

[nrqed]

Homework Statement

A 63.8kg spacewalking astronaut pushes off a 678.0kg satellite, exerting a 156.0N force for the 0.870s it takes him to straighten his arms. How far apart are the astronaut and the satellite after 8.67min?

Homework Equations

The Attempt at a Solution

I tried just finding the acceleration of the satellite using Fnet=ma and then using that acceleration to place it into d=1/2at^2 (assuming the satellite was at rest) The answer came up into the thousands so I knew I did something wrong. I have no idea of how to start this question so it'd be great if someone could help out!

Thanks!

As you said, the satellite's motion is small compared to the one of the astronaut. Most of the separation will be due to the motion of the astronaut, so you should find his/her acceleration. If they want much precision, then you can take into account the displacement of the satellite but it will be small compared to the one of the astronaut.

 

[alexi_b]

As you said, the satellite's motion is small compared to the one of the astronaut. Most of the separation will be due to the motion of the astronaut, so you should find his/her acceleration. If they want much precision, then you can take into account the displacement of the satellite but it will be small compared to the one of the astronaut.

But how can i find the acceleration of the astronaut when I barely know anything about them? Would i just be using Fnet= ma, where m= astronauts mass and Fnet= the force they apply on the satellite?

 

[nrqed]

But how can i find the acceleration of the astronaut when I barely know anything about them? Would i just be using Fnet= ma, where m= astronauts mass and Fnet= the force they apply on the satellite?

Yes. Recall Newton's third law: fi the astronaut pushes on the satellite by 156 N, the force on the astronaut due to the contact with the satellite is also 156 N.

 

[alexi_b]

Yes. Recall Newton's third law: fi the astronaut pushes on the satellite by 156 N, the force on the astronaut due to the contact with the satellite is also 156 N.

Okay gotcha! But if i may ask, what does the time the astronaut have in contact with the satellite have to do with the problem?

 

[nrqed]

Okay gotcha! But if i may ask, what does the time the astronaut have in contact with the satellite have to do with the problem?

The astronaut accelerates only while pushing, so only during this 0.870 s. After he/she loses contact, he/she will continue moving at constant velocity. So you need to find his/her final velocity after being accelerated during 0.870 s. And then you will use that d = vt with t corresponding to the 8.67 min

 

[alexi_b]

The astronaut accelerates only while pushing, so only during this 0.870 s. After he/she loses contact, he/she will continue moving at constant velocity. So you need to find his/her final velocity after being accelerated during 0.870 s. And then you will use that d = vt with t corresponding to the 8.67 min

thanks so much, you've been a great help!

 

[alexi_b]

The astronaut accelerates only while pushing, so only during this 0.870 s. After he/she loses contact, he/she will continue moving at constant velocity. So you need to find his/her final velocity after being accelerated during 0.870 s. And then you will use that d = vt with t corresponding to the 8.67 min

Sorry, just another question came up. Do I assume the astronauts initial velocity is 0? Because other than that I don't see any other way of calculating the astronauts final velocity

 

[nrqed]

Sorry, just another question came up. Do I assume the astronauts initial velocity is 0? Because other than that I don't see any other way of calculating the astronauts final velocity

Good question. Yes, you can. The point is that initially the astronaut is at rest relative to the satellite. In principle it does not have to be this way and the question should have made it clear, but from experience I can tell you that I am sure they assume this.

By the way, I replied to your other question about two blocks on one another.

 

[alexi_b]

Good question. Yes, you can. The point is that initially the astronaut is at rest relative to the satellite. In principle it does not have to be this way and the question should have made it clear, but from experience I can tell you that I am sure they assume this.

By the way, I replied to your other question about two blocks on one another.

I found the acceleration using the astrounaut to be 2.44 m/s^2
So i just used Vf = Vi + at and solved for Vf which turned out to be 2.12 m/s
This will now become my initial velocity of the satellite.

Using D=vt, d=(2.12m/s)(520.2 s) <-- 8.67 min turned into seconds
and i get 1102.824 m

does this seem correct?

 

[nrqed]

I found the acceleration using the astrounaut to be 2.44 m/s^2
So i just used Vf = Vi + at and solved for Vf which turned out to be 2.12 m/s
This will now become my initial velocity of the satellite.

Using D=vt, d=(2.12m/s)(520.2 s) <-- 8.67 min turned into seconds
and i get 1102.824 m

does this seem correct?

Yes, it is right (You meant "initial velocity of the astronaut").