An astronaut is floating in space near her shuttle when she realizes that the cord that's supposed to attach her to the ship has become disconnected. Her total mass (body+suit+equipment) is 91kg. She reaches into her pocket, finds a 1 kg metal tool, and throws it out into space with a velocity of 6m/s directly away from the ship. if the ship is 10 m away, how long will it take her to reach it?

Explanation

Here, the astronaut+tool are the system. Because of conservation of linear momentum ltbgt `m_("astronaut")v_("astronaut")+m_("tool")v_("tool")=0`
`m_("astronaut")v_("astronaut")=-m_("tool")v_("tool")`
`v_("astronaut")=-(m_("tool"))/(m_("astronaut"))v_("tool")`
`=-(1kg)/(90kg)(-6m//s)=(1)/(15)m//s`
Using distance=rate`xx`time, we find
`t=(d)/(v)=(10m)/((1)/(15)m//s)=150s=2(1)/(2)`min