Momentum, Impulse, Collision...?

Question

You have been hired to check the technical correctness of an upcoming TV mystery, "Mari Mar in Space". The mystery takes place in the space shuttle. In one scene, the astronaut Mari Mar’s safety line is sabotaged while she is on a space walk, so she is no longer connected to the space shuttle. She checks and finds that her thruster pack has also been damaged and no longer works. She is 200 meters from the shuttle and moving with it. That is, she is not moving with respect to the shuttle. There she is drifting in space with only 4 minutes of air remaining. To get back to the shuttle, she decides to unstrap her 10-kg tool kit and throw it away with all her strength, so that it has speed of 8 m/s. In the script, she survives, but is this correct? Her mass, including space suit, is 80 kg.

Pls show all necessary calculations with explanations pls, best answers gets 10 points...

Answer 1

Oooo...do I get royalties as the technical adviser for the script?

Anyhooo...Mv = mV; where M = 80 kg (she and the suit) and m = 10 kg, the tossed tool kit (with her lipstick inside). V = 8 mps, with her Herculean hurl; so that v = mV/M = 10*8/80 = 1 mps. As she is S = 200 m away, she would float for S/v = 200/1 = 200 sec = t. As 4 minutes is 240 sec, she has 40 sec to enjoy the view from outside before ducking inside for a breather.

And the heroine survives yet another close one...whew. But next episode....

Answer 2

I've been out of the physics game for a little while so it took me a little longer than usual to solve this problem. According to my calculations it turns out that Mari Mar does indeed survive her bout with the cosmos. First off I used conservation of momentum to determine Mari Mar's velocity after she threw her tool kit:
[M(m)+M(t)](v)=M(m)V+M(t)v
Since Mari Mar is initially at rest and after some algebra you get:
-M(m)V=M(t)v
Now you can solve for the unknown V, getting:
V= -M(t)v/M(m)
Plugging in all the values you get
V= -(10kg)(8m/s)/(80kg)
V= -1m/s
With the negative sign now you know that she is traveling back towards the spaceship at a rate of one meter per second. She only has 4 minutes left until her oxygen is depleted, using some kinematics we'll be able to see that she indeed survives.
x=vt
Distance=velocity x time
Solving for t:
t=x/v
t=200m/1m/s
t=200s
Since she has 4 minutes left to live, with some simple converting you'll see that she gets back to the space shuttle with 40 seconds to spare.