A ball with a mass of # 6 kg# is rolling at #6 m/s# and elastically collides with a resting ball with a mass of # 8 kg#. What are the post-collision velocities of the balls?

1 Answer
Mar 28, 2016

Answer:

#v_1^'=-6/7 " "m/s#

#v_2^'=36/7 " "m/s#

Explanation:

#m_1*v_1+m_2*v_2=m_1*v_1^'+m_2*v_2^'#
#6*6+8*0=6*v_1^' + 8*v_2^'#
#36+0=6*v_1^'+8*v_2^'#
#36=6*v_1^'+8*v_2^'" "(1)#

#" we use the equation " v_1+v_1^'=v_2+v_2^'#
#" for calculating velocities after collision"#

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

#36=6*v_1^'+8(6+v_1^')#
#36=6*v_1^'+48+8*v_1^'#
#36-48=14*v_1^'#
#-12=14*v_1^'#
#v_1^'=-12/14=-6/7 " "m/s#

#"use (2)"#
#6-6/7=v_2^'#
#(42-6)/7=v_2^'#

#v_2^'=36/7" " m/s#