Physics 30 question about conservation of momentum

[RRmy0440]

Homework Statement

A space person is motionless a distance of 500m away from the safety of the spacecraft . The person has exactly 11.32min of air left and the person's mass is 103.2kg, including equipment. The person throws a phaser at a velocity of 50.2km/h away from the spacecraft in order to get back. I f the mass of the phaser is 5.3 kg, how many minutes of extra air does the person have when they get back to the spacecraft ？(Ans: 0.28min)

I attempted to solve it , but get the answer of 0.25min.

please help！

T

Homework Equations

Conservation and momentum.
P=mv
Ft=mv
Impulse momentum theory

The Attempt at a Solution

① m1v1+m2v2=m1v1'+m2v2'
v1'=42.97m/min

②t=500/(836.9m/min+42.97m/min) ＝0.57min

③d=v1't=42.97m/min *0.57min=24.42m
④d(remaining)=500m-24m=475.6m
⑤t=d/v=475.6m/ (42.97m/min)=11.07min
⑥t(remaining)=11.32-11.07=0.25min

I try to solve the question, but got the wrong answer. Could anyone help me out？ Thank you so much.

 

[haruspex]

m1v1+m2v2=m1v1'+m2v2'

What values are you using for m1 and m2 here?

②t=500/(836.9m/min+42.97m/min) ＝0.57min

Please explain this calculation.

 

[verty]

I would leave it in km/h till the latest possible moment (unless you've been taught differently).

 

[RRmy0440]

What values are you using for m1 and m2 here?

Please explain this calculation.

d=500m
t1=11.32min
m1=103.2kg
m2=5.3kg
v2'=50.2km/h=836.7m/min

 

[RRmy0440]

I would leave it in km/h till the latest possible moment (unless you've been taught differently).

If you would like to solve it with the unit km/h , please feel free to do that.

 

[RRmy0440]

So do you think I am on the right track of solving this？

 

[verty]

It's up to you what way you want to solve it. By the way, I got a different answer: 0.31. I don't think 0.28 is correct.

PS. Your way of doing it is confusing to me so I won't comment anymore.

 

[haruspex]

m1=103.2kg

That is the mass of the astronaut including all equipment.
I still do not see any explanation for your equations.

Also, why do you add the two speeds?

 

[haruspex]

I got a different answer: 0.31. I don't think 0.28 is correct.

I get 0.28. Check you did not get -0.31. If you did, see the bold text in my post #8.

 

[RRmy0440]

I get 0.28. Check you did not get -0.31. If you did, see the bold text in my post #8.

Can you please explain how did you get the right answer？

 

[RRmy0440]

That is the mass of the astronaut including all equipment.
I still do not see any explanation for your equations.

Also, why do you add the two speeds?

Does it mean that the phaser is also included to have the total mass of 103.2kg？

For the reason why I added the two speeds together...I think I had been misled by another question I just done

 

[RRmy0440]

Thank you guys, i get the right answer.