Problem 8.49

8.49.

The recoil velocity of the astronaut can be obtained from the conservation of momentum.

p_i  =  p_f

$0 ~=~ (80 kg)(\vec{v_{r}}) + (.5 kg)(20 m/s \hat{i})$

$\vec{v_{r}} ~=~ - .125 m/s \hat{i}$

If we solve for the time that it takes her to get back the 30 m to her ship, we find

$t ~=~ \frac{30 m}{.125 m/s} ~=~ 240 s$