An astronaut on a space walk bumps the shuttle and starts moving away at a velocity of 0.02m/s. The astronaut's mass is 100kg. He takes a 1kg "safety weight" and shoves it away in exactly the direction of his motion at a speed of 6m/s. at what speed does the astronaut move back towards the space shuttle.
To solve this problem, we can use the concept of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event in the absence of external forces.
Here's how we can apply this concept to determine the speed at which the astronaut moves back towards the space shuttle:
1. Calculate the initial momentum of the system: The initial momentum of the system is the momentum of the astronaut before pushing the safety weight.
Initial momentum of the system = Mass of the astronaut × Velocity of the astronaut
Momentum = 100 kg × 0.02 m/s = 2 kg⋅m/s
2. Calculate the momentum of the safety weight after being pushed: The momentum of the safety weight is given by the product of its mass and velocity.
Momentum of the safety weight = Mass of the safety weight × Velocity of the safety weight
Momentum = 1 kg × 6 m/s = 6 kg⋅m/s
3. According to the conservation of momentum, the total momentum after the event should be equal to the initial momentum. Since the astronaut and the safety weight are moving in opposite directions, the momentum of the safety weight should have a negative sign.
Total momentum after the event = (Momentum of the astronaut) + (Momentum of the safety weight)
2 kg⋅m/s = (Mass of the astronaut × Velocity of the astronaut) + (-Mass of the safety weight × Velocity of the safety weight)
4. Rearrange the equation and solve for the velocity of the astronaut.
Velocity of the astronaut = (2 kg⋅m/s + 6 kg⋅m/s) / (Mass of the astronaut)
Velocity of the astronaut = 8 kg⋅m/s / 100 kg = 0.08 m/s
Therefore, the astronaut moves back towards the space shuttle at a speed of 0.08 m/s.