An astronaut with a mass of #75 kg# is floating in space. If the astronaut throws a #7 kg# object at a speed of #5/4 m/s#, how much will his speed change by?

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Answer 1 · 2016-05-13T19:43:50

#vec v_a^'=-0.12" " m/s#

#"momentum before event:"#
#.............................................#

#vec P_a=m_a*vec v_a" momentum of astronaut"#
#vec P_a=75*0=0#

#vec P_o=m_o*vec v_o" momentum of object "#
#vec P_o=7*0=0#

#Sigma P_b=0+0=0" total momentum"#

#"momentum after event:"#
#...........................................#

#P_a^'=m_a*v_a^'#
#vec P_a^'=75*vec v_a^'#

#vec P_o^'=m_o*vec v_o^'#
#vec P_o^'=7*5/4=35/4" " kg*m/s#

#Sigma vec P_a=P_a^'+P_o^'#
#Sigma vec P_a=75*vec v_a^'+35/4#

#"in this event momentum is conserved"#
#...............................................................#

#Sigma vec P_b=Sigma vec P_a#
#0=75*vec v_a^'+35/4#

#75*vec v_a^'=-35/4#

#vec v_a^'=-35/300#

#vec v_a^'=-0.12" " m/s#