An astronaut with a mass of #90 kg# is floating in space. If the astronaut throws an object with a mass of #5 kg# at a speed of #3/4 m/s#, how much will his speed change by?

1 Answer
Jul 1, 2016

#v_a^'=-0.04" "m/s#

Explanation:

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#"Before event:"#
#P_a=m_a*v_a#
#P_a:"momentum of astronaut"#
#m_a:"mass of astronaut"#
#v_a:"velocity of astronaut"#
#P_a=90*0=0#

#P_o=m_o*v_o#
#P_o:"momentum of object"#
#m_o:"mass of object"#
#v_o:"velocity of object"#
#P_o=5*0=0#

#P_b=P_a+P_o=0" total momentum"#

#"After event:"#
#P_a'=m_a*v_a'#
#P_a^'=90*v_a^'#

#P_o=m_o*v_o^'#
#P_o=5*3/4=15/4#

#0=90*v_a^'+15/4#

#90*v_a^'=-15/4#

#v_a^'=-15/(90*4)#

#v_a^'=-1/(6*4)=-1/24#

#v_a^'=-0.04" "m/s#