An astronaut with a mass of #90 kg# is floating in space. If the astronaut throws an object with a mass of #7 kg# at a speed of #2/9 m/s#, how much will his speed change by?

1 Answer
May 7, 2017

#"the change of speed of astronaut is :" v_a=-0.02 m/s#

Explanation:

#m_a:90 kg" mass of astronaut "#
#m_o:7 kg" mass of object"#

#"let total momentum before thrown the object be "Sigma P_b#

#v_a:0" speed of astronaut"#
#v_o:0" speed of object"#

#Sigma P_b=m_a*v_a +m_o*v_0#
#v_a=0" , "v_o=0#
#Sigma P_b=90*0+7*0=0#

#"let total momentum after thrown the object be "Sigma P_a#

#u_a:?"speed of astronaut after thrown the object"#
#u_o:2/9 m/s" speed of object thrown."#

#Sigma P_a=m_a*u_a+m_o*u_o#
#Sigma P_a=90*u_a+7*2/9#
#Sigma P_a=90*u_a+14/9#

#"According to the principle of momentum conservation, the total"# #"momentum before the object is thrown is equal to the total"# #"momentum after the object is thrown."#

#Sigma P_b=Sigma P_a#
#0=90*u_a+14/9#
#90*u_a=-14/9#
#u_a=-14/(90*9)#
#u_a=-14/810#
#u_a=-0.02 m/s" rounded the two decimal place."#

#"Minus sign tells us that the direction of the speed of astronaut "#
#"is opposite to the direction of the speed of object."#