Conservation of Momentum and the Spaceman's Return to His Craft

[MagikalGiant]

Homework Statement

So I was revising for some tests I've got coming up in July, when I came across this question in the book. It kinda puzzled me, so here I go...

Spoiler

An astronaut of mass 100kg is adrift in space. He is 10m from his spacecraft . To get back he throws a spanner of mass 1.0kg directly away from the craft at speed 5.0ms^-1.
a) Explain why he moves back towards his spacecraft .
b) Calculate how long it will take him to reach the craft.

Now part a) is the easy part, we all know that "momentum before = momentum after" as it's the conservation of momentum law - and so in throwing the spanner, he moves back to his craft (albeit slowly).

My beef is with part b), the time it takes him to do so...

Homework Equations

Momentum = Mass x Velocity.
p=mv

Velocity = Displacement / Time
v = s/t

The Attempt at a Solution

So we have the conservation of momentum, which would be awesome to use right now - but it doesn't work. The total momentum before would be...

Spanner's momentum = mv = 1kg x 0m/s = 0kg/ms
Astronaut's momentum = mv = 100kg x 0m/s = 0kg/ms
So the momentum before is 0ms^-1?
This would make the momentum after = 0, also. So he doesn't get anywhere?

I also tried using v=s/t, as we have s and we need t, but we don't have the v...

The book seems to think it's 200 seconds, but I'm a bit confused as I don't think I have the right information. It's really annoying, though, because I think it might be something simple I'm not thinking about.

Thanks for the help, MagikalGiant.

 

[tiny-tim]

Welcome to PF!

Hi MagikalGiant! Welcome to PF!

So the momentum before is 0ms^-1?
This would make the momentum after = 0, also. So he doesn't get anywhere?

The total momentum after is 0.

So the astronaut's momentum after is … ?

 

[ashishsinghal]

conservation of momentum states that the net momentum OF SYSTEM is conserved.
I think you are using it for spanner and astronaut separately.