motionless 100 kg astronaut is holding a 12 kg tool while on a spacewalk. To get moving, the astronaut throws the tool forward at a speed of +6.6 m/s. How fast does the astronaut move backward?
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the throw is equal to the total momentum after the throw.
Before the throw, both the astronaut and the tool are at rest, so their total momentum is zero.
After the throw, the tool moves forward with a mass of 12 kg and a speed of +6.6 m/s. Therefore, the momentum of the tool is 12 kg * 6.6 m/s = 79.2 kg*m/s.
To ensure the total momentum is conserved, the astronaut must move backward with a momentum of -79.2 kg*m/s.
Since the astronaut's mass is 100 kg, we can calculate the speed at which the astronaut moves backward by dividing the momentum by the mass. Hence, the speed of the astronaut moving backward is -79.2 kg*m/s / 100 kg = -0.792 m/s.
Therefore, the astronaut moves backward at a speed of -0.792 m/s.