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.
To solve this problem, we need to use the law of conservation of momentum. According to this law, the total momentum before an event is equal to the total momentum after the event, assuming no external forces are acting on the system.
Here's how we can approach this problem step by step:
Step 1: Calculate Sally's momentum before throwing the tool kit
Sally's momentum before throwing the tool kit is given by the formula:
momentum = mass × velocity
Given that the combined mass of Sally and her spacesuit is 97 kg and assuming she is at rest relative to the spaceship, her initial momentum is 0 kg·m/s.
Step 2: Calculate the spaceship's momentum after Sally throws the tool kit
Since there are no external forces acting on the system, the combined momentum of Sally and the spaceship must be conserved.
After throwing the tool kit, Sally gains momentum in one direction, while the spaceship gains an equal amount of momentum in the opposite direction to conserve the total momentum.
Given that the mass of the tool kit is 14 kg and Sally initially has no momentum, the momentum of the spaceship after Sally throws the tool kit is:
momentum = mass × velocity
Let's say Sally throws the tool kit with a velocity of v m/s. The mass of the spaceship is unknown, but we can use the mass of Sally and the tool kit to express the spaceship's momentum. The initial momentum of Sally and the tool kit is (97 kg + 14 kg) × 0 kg·m/s = 0 kg·m/s. Therefore, the final momentum of the spaceship after Sally throws the tool kit would also be 0 kg·m/s.
The formula for the momentum of the spaceship is:
momentum = mass × velocity
0 kg·m/s = (mass of spaceship) × (-v m/s)
Since the spaceship's change in momentum is equal to zero, we can conclude that the mass of the spaceship multiplied by its velocity must also be equal to zero.
Step 3: Calculate the minimum speed at which Sally has to throw the tool kit to get back to the spaceship in time
In order for Sally to reach the spaceship before her oxygen supply is exhausted, she needs to reduce her distance from the spaceship to zero. This means she needs to change her velocity from 0 m/s to the same velocity as the spaceship.
Therefore, the minimum speed at which Sally has to throw the tool kit is equal to the velocity of the spaceship, which we'll call V.
Using the formula for momentum,
momentum = mass × velocity
0 kg·m/s = (97 kg + 14 kg) × (-V m/s)
Simplifying the equation, we get:
0 = 111 kg × (-V)
Since we want to find the minimum speed, V, we can ignore the negative sign.
0 = 111 kg × V
Solving for V, we find that V = 0 m/s.
The minimum speed at which Sally can throw the tool kit in order to get back to the spaceship before her oxygen supply is exhausted is 0 m/s. This means she doesn't need to throw the tool kit at all to get back to the spaceship.