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.

 

[tomcue]

Hi there! It looks like you've done a great job setting up the problem and using the appropriate equations. However, there seems to be a small error in your calculations. When you calculated the acceleration, you used a negative sign in front of the velocity term (vf^2-vo^2)/2x. This is because the man is moving in the opposite direction of the object he threw, so his velocity is negative. However, when you calculated the time, you used a positive sign in front of the velocity term (vf-vo)/a. This should also be negative, as the man is moving in the opposite direction of the object. This small error results in your final answer being twice the correct value. If you make this correction, you should get the correct answer of 800 seconds. Keep up the good work!