Conservation of momentum problem and kinematics ?

[mychellbella]

Conservation of momentum problem and kinematics!?

Hi, I've been working on this problem for the last three hours, I hope someone can help. In fact, the solution I keep getting is double the correct answer (the answers are in the back of the book, but not the how).
An 80 kg astronaut is stranded 10 m from his spaceship in free space. In order to get back to his ship, he throws a 2.0 kg piece of equipment w/ a speed of 0.5 m/s directly away from the ship. How long will it take for him to reach the ship?

man object
m1=80kg m2= 2.0kg
vo1=0 vo2= 0
vf1= ? vf2= .5m/s

so, i started by treating this like a gun and bullet problem since he will be recoiling.

Pf(momentum final) = Po (momentum orignal) = 0

Pf=m1vf1+ m2vf2
0= m1vf1 +m2vf2
vf1= (-m2/m1)*vf2
vf1=(-2.0kg/80kg)*.5m/s
vf1= .0125 m/s

okay, now i find the acceleration, so i can then use a kinematic equation to find the time. I only use the info for the man and vo is .0125 m/s and vf=0. x=10m.

a=(vf^2-vo^2)/2x
a=(0-.0125m/s^2)/2(10m)
a=-7.81*10^-6 m/s^2

t=(vf-vo)/a
t=(0-.0125m/s)/-7.81*10^6 m/s^2
t =1600 seconds

The problem, is that the book is saying the anwer is 800 seconds. What am I doing wrong! Please help! thank you!

 

[rl.bhat]

Hi mychellbella, welcome to PF.
No external force is acting on the astronaut in the direction of his motion. So after throwing the packet, he will move with the uniform velocity.