A ball with a mass of # 5 kg# is rolling at #8 m/s# and elastically collides with a resting ball with a mass of #4 kg#. What are the post-collision velocities of the balls?

1 Answer
May 23, 2016

Answer:

#v_1^'=8/9 " "m/s#

#v_2^'=80/9" "m/s#

Explanation:

#m_1=5" "kg#
#v_1=8" "m/s#
#P_1=m_1*v_1=5*8=40" " kg*m/s#

#m_2=4" "kg#
#v_2=0#
#P_2=m_2*v_2=4*0=0#

#Sigma P_b=P_1+P_2" total momentum"#
#Sigma P_b=40+0=40" "kg*m/s #

#"post collision velocities :"#

#v_1^'=(2*Sigma P_b)/(m_1+m_2)-v_1#

#v_1^'=(2*40)/(5+4)-8#

#v_1^'=80/9-8#

#v_1^'=(80-72)/9#

#v_1^'=8/9 " "m/s#

#v_2^'=(2*Sigma P_b)/(m_1+m_2)-v_2#

#v_2^'=(2*40)/(5+4)-0#

#v_2^'=80/9" "m/s#