Can an Astronaut Survive by Throwing a Toolkit in Space?

[ppl k1ll3r]

Homework Statement

You have been hired to check the technical correctness of an upcoming made-for-TV murder mystery. The mystery takes place in a space shuttle. In one scene, the astronaut'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. The 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 a speed of 8 m/s. In the script, she survives, but is this correct? Her mass, including the space suit, is 80 kg. (Yes she does survive)

Homework Equations

p = mv
v = d/t
p = p'

The Attempt at a Solution

My attempt:

p = p', initial momentum 0 with respect to space shuttle
0 = m2Vfinal + (mkit)(Vkit)
0 = (70)Vfinal + (10)(8)
Vfinal = -1.14 m/s

V = 1.14 m/s
d = 200m

t = d/t
= 175 s

Time she has = 4 min
= 240 s

Therefore, she does survive.

I'm pretty sure I did it wrong though. Because the negative velocity doesn't make sense. Both the kit and her move in the same direction. Any1 wana help?

 

[Pengwuino]

Negative velocities are acceptable. Remember, a velocity is a vector so it can be positive or negative. In this case, it just means your moving in the opposite direction (assuming you picked the toolbelt to travel in the positive direction). Of course if you're adding 2 numbers together to get 0 and the mass is always positive, one definitely needs to be negative. The problem looks correct.

Also, the kit and her do NOT move in the same direction. If that were the case, momentum would not be conserved.

 

[ppl k1ll3r]

Negative velocities are acceptable. Remember, a velocity is a vector so it can be positive or negative. In this case, it just means your moving in the opposite direction (assuming you picked the toolbelt to travel in the positive direction). Of course if you're adding 2 numbers together to get 0 and the mass is always positive, one definitely needs to be negative. The problem looks correct.

Also, the kit and her do NOT move in the same direction. If that were the case, momentum would not be conserved.

But say everything is stationary, then she throws the kit, doesn't that cause her to move in the same direction as the throwing movement pulls her forward? I can't really visualize this.
Also, can you expand on why those 2 things moving in same direction would not result in the conservation of momentum? I really need to understand this topic. This is going to be an easy problem compared to the questions our grade 12 teacher puts on the test.

 

[Pengwuino]

But say everything is stationary, then she throws the kit, doesn't that cause her to move in the same direction as the throwing movement pulls her forward? I can't really visualize this.
Also, can you expand on why those 2 things moving in same direction would not result in the conservation of momentum? I really need to understand this topic. This is going to be an easy problem compared to the questions our grade 12 teacher puts on the test.

Ok so everything is stationary, that is the total momentum is 0. Setup your coordinate system with the astronaut at the origin on the x-axis and the direction they want to throw it, let's say the left, along the negative x-axis. When she throws the kit to the left, the kit has momentum p = mv. v here is -8m/s because its going in the negative x-direction. Her momentum would be p = mv = (-8m/s) * (10kg). Now for momentum to be conserved, the total momentum after her throwing it has to equal 0 since that was the momentum before she threw it. In order to make up for this -80 kg*m/s momentum, she needs to have a positive 80 kg*m/s momentum so that they sum to 0 thus conserving momentum. Since her mass is always positive and in this case, 80kg, the velocity must be positive as well.

The way you setup your program is that the direction away from her was positive and the direction towards the shuttle was negative. In my example, the directions were switched (ie she went a positive velocity and the kit went with a negative velocity) but the idea is the same.

 

[ppl k1ll3r]

Thanks, makes sense now.