Astronaut Jennifer's lifeline to her spaceship comes loose and she finds herself stranded, "floating" 100 m from the mothership. She suddenly throws her 2.00-kg wrench at 20 m/s in a direction away from the ship. If she and her spacesuit have a combined mass of 200 kg, how long does it take her to coast back to her spaceship?

Question

Astronaut Jennifer's lifeline to her spaceship comes loose and she finds herself stranded, "floating"  100 m from the mothership. She suddenly throws her  2.00-kg wrench at  20 m/s in a direction away from the ship. If she and her spacesuit have a combined mass of  200 kg, how long does it take her to coast back to her spaceship?

Quizplus · Accepted Answer

To solve this problem, we use the conservation of momentum principle. The momentum before and after Jennifer throws the wrench must be equal because there are no external forces acting on the system. The momentum of the wrench is given by its mass times its velocity (2.00 kg * 20 m/s = 40 kg*m/s). Since momentum is conserved, the momentum of Jennifer moving towards the spaceship must also be 40 kg*m/s. To find her velocity, we divide the momentum by her mass (40 kg*m/s / 200 kg = 0.2 m/s). To find the time it takes her to travel 100 m at this speed, we divide the distance by her velocity (100 m / 0.2 m/s = 500 s).

Astronaut Jennifer's Lifeline to Her Spaceship Comes Loose and She