an astronaut on a space walk bumps the shuttle and starts moving away at a velocity of 0.02m/s. The astronauts mass is 100kg. He has takesa 1kr "safety week" and shoves it away in exactly the direction of his motion at a speed of 6m/s. what speed does the astronaut move back toward the space shuttle.

To find the speed at which the astronaut moves back toward the space shuttle, we can use the principle of conservation of momentum. The total momentum before the astronaut shoves the 1kg "safety week" can be calculated by adding the momentum of the astronaut and the momentum of the "safety week" together.

The momentum of an object is given by the product of its mass and velocity. The momentum of the astronaut before shoving the "safety week" can be calculated as follows:

P(astronaut) = mass(astronaut) * velocity(astronaut)

P(astronaut) = 100 kg * 0.02 m/s

P(astronaut) = 2 kg·m/s

Now, let's calculate the momentum of the "safety week":

P(safety week) = mass(safety week) * velocity(safety week)

P(safety week) = 1 kg * 6 m/s

P(safety week) = 6 kg·m/s

Since momentum is conserved, the total momentum before and after the shove should be the same. Therefore, the momentum of the astronaut and the "safety week" after the shove should add up to 2 kg·m/s + 6 kg·m/s = 8 kg·m/s.

Now, we need to find the velocity at which the astronaut moves back toward the space shuttle. This can be done by dividing the total momentum by the mass of the astronaut:

velocity(astronaut) = total momentum / mass(astronaut)

velocity(astronaut) = 8 kg·m/s / 100 kg

velocity(astronaut) ≈ 0.08 m/s

Therefore, the astronaut moves back toward the space shuttle at a speed of approximately 0.08 m/s.