A ball with a mass of # 5 kg# is rolling at #5 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 28, 2016

Answer:

#v_1^'=5/9" "m/s#

#v_2^'=50/9" "m/s#

Explanation:

#m_1=5" " kg#
#vec v_1=5 " "m/s#

#vec P_1=m_1*vec v_1#
#vec P_1=5*5=25 " "kg*m/s" momentum before collision for object " m_1#

#m_2=4" "kg#
#vec v_2=0#

#vec P_2=m_2*vec v_2=4*0=0" the object with " m_2= 4 kg" has no momentum"#

#Sigma vec P_b=25+0=25 " "kg*m/s" total momentum before collision"#

#"post collision velocity of object with "m_1="5 kg"#

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

#v_1^'=(2*25)/(5+4)-5#

#v_1^'=50/9-5#

#v_1^'=50-45/9#

#v_1^'=5/9" "m/s#

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

#v_2^'=(2*25)/(5+4)-0#

#v_2^'=50/9" "m/s#