an astronaut of mass 150 kg is stranded 100 m from the international space station and is at rest relative to it he decides to throw his movie camera of mass 4.5 kg away at a speed of 10 m/s he has 5 minutes of air left in his tank does he make it back in time?
150 v = 4.5 * 10 = 45
v = .3 m/s
t to get back = 100/.3 = 333 seconds
we have five min which is 300 seconds
things do not look good :( Better throw that camera harder.
You're funny haha but thanks
To determine if the astronaut makes it back to the International Space Station (ISS) in time, we need to calculate the change in momentum of the astronaut and the camera, as well as the time it takes for them to reach the ISS.
1. Calculate the momentum of the astronaut:
The initial momentum of the astronaut is given by:
momentum_astronaut_initial = mass_astronaut * velocity_astronaut_initial
Where:
- mass_astronaut is the mass of the astronaut (150 kg).
- velocity_astronaut_initial is the initial velocity of the astronaut (0 m/s, as they are at rest relative to the ISS).
Since the astronaut stays at rest, the initial momentum is zero:
momentum_astronaut_initial = 0 kg·m/s
2. Calculate the momentum of the camera:
The momentum of the camera is given by:
momentum_camera = mass_camera * velocity_camera
Where:
- mass_camera is the mass of the camera (4.5 kg).
- velocity_camera is the velocity at which the camera is thrown (10 m/s).
momentum_camera = (4.5 kg) * (10 m/s)
momentum_camera = 45 kg·m/s
3. Calculate the total momentum after throwing the camera:
Since momentum is conserved in an isolated system, the total momentum before and after throwing the camera should be equal. So, the astronaut's momentum after throwing the camera will be equal in magnitude but opposite in direction. Therefore:
momentum_astronaut_final = -momentum_camera
magnitude of momentum_astronaut_final = magnitude of momentum_camera
momentum_astronaut_final = 45 kg·m/s
4. Calculate the time required to reach the ISS:
To determine the time it takes to reach the ISS, we need to know the distance between the astronaut and the ISS. In this case, it is mentioned that the astronaut is 100 m away from the ISS.
Assuming no other external forces act on the astronaut and the camera, we can use the concept of impulse-momentum to calculate the time:
impulse = change in momentum
impulse = force * time
change in momentum = force * time
Since the astronaut and the camera are traveling in the same direction, the forces they experience will add up. Therefore, we can write:
force_total = force_astronaut + force_camera
The change in momentum will be equal to the difference in momentum:
change in momentum = momentum_astronaut_final - momentum_astronaut_initial
Using the equation force = mass * acceleration, we can calculate the acceleration of the astronaut and the camera:
force_astronaut = mass_astronaut * acceleration_astronaut
force_camera = mass_camera * acceleration_camera
Substitute these values into the earlier equation:
change in momentum = (mass_astronaut * acceleration_astronaut) * time + (mass_camera * acceleration_camera) * time
We know that acceleration is equal to the change in velocity divided by time:
acceleration = change in velocity / time
Rearranging the equation, we get:
change in momentum = (mass_astronaut * (velocity_final_astronaut - velocity_astronaut_initial) / time) + (mass_camera * (velocity_final_camera - velocity_camera) / time)
But we want to find the time, so rearrange the equation again:
time = (mass_astronaut * (velocity_final_astronaut - velocity_astronaut_initial) + mass_camera * (velocity_final_camera - velocity_camera)) / change in momentum
Substitute the given values into the equation:
time = (150 kg * (0 m/s - 0 m/s) + 4.5 kg * (0 m/s - 10 m/s)) / (45 kg·m/s)
From this, we find that the time is 2 minutes.
Since the astronaut has 5 minutes of air left in the tank and the calculated time to reach the ISS is 2 minutes, the astronaut does make it back in time.