A ball with a mass of #8 kg# moving at #4 m/s# hits a still ball with a mass of #3 kg#. If the first ball stops moving, how fast is the second ball moving?

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Answer 1 · 2016-05-11T15:18:59

#v_1^'=20/11 m/s#

#v_2^'=64/11 m/s#

#"Before collision:"#
#...........................................................#
#vec P_1=m_1*vec v_1" (momentum for the first object)"#

#vec P_1=8*4=32 kg*m/s#

#vec P_2=m_2*vec v_2"(momentum for the second object)"#

#vec P_2=3*0=0#

#Sigma vec P_b=vec P_1 +vec P_2#
#Sigma vec P_b=32+0=32" " kg*m/s#

#"After collision :"#
#".............................................................."#

#vec P_1^'=m_1*vec v_1^'"#
#vec P_2^'=m_2*vec v_2^'#

#Sigma vec P_a=vec P_1^'+vec P_2^'#
#Sigma vec P_a=8*v_1^'+3*v_2^'#

#"Conservation of momentum:"#
#...............................................................#
#Sigma vec P_b=Sigma vec P_a#

#32=8v_1^'+3v_2^'" "(1)"#

#v_1+v_1^'=v_2+v_2^'#

#4+v_1^'=0+v_2^' " "(2)#

#32=8v_1^'+3(4+v_1^')#

#32=8v_1^'+12+3v_1^'#

#32-12=11v_1^'" ; "20=11v_1^'#

#v_1^'=20/11 m/s#

#"using equation (2):"#

#4+20/11=v_2^'#

#v_2^'=64/11 m/s#