Answer :
Final answer:
When the astronaut throws away the wrench, their resulting velocity in the opposite direction is -0.28 m/s.
Explanation:
The astronaut and equipment weigh 2,156 N on Earth. In space, the astronaut is weightless and throws away a 5.0 kg wrench with a velocity of 5.0 m/s. To find the resulting velocity of the astronaut in the opposite direction, we can use the principle of conservation of momentum. Since momentum is conserved in an isolated system, the momentum of the astronaut before throwing the wrench must be equal to the momentum of the astronaut and the wrench after the throw.
The momentum before the throw is the product of the astronaut's mass and velocity, which is 90 kg * 0 m/s = 0 kg·m/s. The momentum after the throw is the sum of the momentum of the astronaut and the momentum of the wrench. The momentum of the wrench can be calculated using the equation momentum = mass * velocity, which is 5.0 kg * -5.0 m/s = -25 kg·m/s (negative sign indicates opposite direction).
Therefore, the resulting momentum of the astronaut in the opposite direction is 0 kg·m/s - 25 kg·m/s = -25 kg·m/s. The resulting velocity can be found by dividing the momentum by the mass of the astronaut, which is -25 kg·m/s / 90 kg = -0.28 m/s (negative sign indicates opposite direction).
