An astronaut with a mass of #85 kg# is floating in space. If the astronaut throws an object with a mass of #5 kg# at a speed of #1/4 m/s#, how much will his speed change by?

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Answer 1 · 2016-05-16T08:34:13

#v_a^'=-0.015" " m/s#

#m_a=85 " "kg " mass of astronaut"#

#v_a=0" velocity of astronaut before event"#

#P_a=m_a*v_a=85*0=0" momentum of astronaut before event"#

#m_o=5" "kg#

#v_o=0" velocity of object before event"#

#P_o=m_o*v_o=5*0=0" momentum of object before event"#

#P_i=P_a+P_o" "P_i=0 " total momentum before event"#

#v_a^'="velocity of astronaut after event"#

#P_a^'=m_a*v_a^'=85*v_a^'" momentum of astronaut after event"#

#P_o^'=m_o*v_o^'=5*1/4=5/4 kg*m/s" object's momentum after event"#

#P_f=P_a^'+P_o^'#

#P_f=85*v_a^'+5/4" total momentum after event"#

#P_i=P_a#

#0=85*v_a^'+5/4#

#85*v_a^'=-5/4#

#v_a^'=-5/(85*4)#

#v_a^'=-0.015" " m/s#