Astronaut Jennifer's lifeline to her spaceship comes loose and she finds herself stranded, "floating" 100. m from the mothership. She throws her 2.00 kg wrench at 20.0 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?
A) 500. s
B) 250. s
C) 2.50 minutes
D) 750. s
E) 1000. s

Question

Quizplus · Accepted Answer

To solve this, 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 $p = mv = 2.00\, \text{kg} \times 20.0\, \text{m/s} = 40.0\, \text{kg}\cdot\text{m/s}$. Since momentum is conserved, Jennifer's momentum in the opposite direction will also be $40.0\, \text{kg}\cdot\text{m/s}$. Her velocity $v$ can be found using $p = mv$, so $v = \frac{p}{m} = \frac{40.0\, \text{kg}\cdot\text{m/s}}{200.0\, \text{kg}} = 0.2\, \text{m/s}$. To find the time $t$ it takes to travel back to the spaceship, we use $t = \frac{d}{v} = \frac{100.0\, \text{m}}{0.2\, \text{m/s}} = 500\, \text{s}$.

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