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?

Question

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?

Emily Abbate · Accepted Answer

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

Sebastian Acosta · Answer

undefined The astronaut's speed will change by approximately 0.0185 m/s.