physics
posted by Sandhya on .
You are hired to check the technical validity of a futuristic
space mystery production. The scene takes place during the
rst manned trip to Pluto's moon, Charon. Sally Skywalker
is outside the spaceship repairing some hardware, when her
safety line to the spaceship mysteriously breaks. Her thruster
pack also is damaged, so she has no obvious means of propul
sion. She is at rest relative to the spaceship, 200 meters away
from it, with only 7 minutes of oxygen left in her life support
pack. To get back to the ship, she decides to remove her tool
kit and throw it away. Assuming that the combined mass
of Sally and her spacesuit is 97 kg and the mass of the tool
kit is 14 kg, what is the minimum speed that she can throw
the tool kit, in order to get back to the spaceship before her
oxygen supply is exhausted?

Use conservation of momentum. I will be happy to check your work.

Initial momentum = 0
Velocity with which skywalker should mve before oxygen exhausts = u
= 200/7*60 = 0.48 m/s
Velocity of throw of kit = v
Mass of skywalker = M = 97 kg
Mass of kit =m = 14 kg
Final momentum = Mu + mv = 97*0.48 + 14v
v = 97*0.48/14 = 0.016 m/s
Is my working correct? 
7 min = 420 s.
She needs to acquire a velocity towards the ship of 200m/420s = 0.48 m/s
0.48*97 = 14 v
v = 3.3 m/s
Right formula, wrong arithmetic 
Thanks a lot for pointing out the arithmetic mistake.