A ball with a mass of # 5 kg# is rolling at #6 m/s# and elastically collides with a resting ball with a mass of #3 kg#. What are the post-collision velocities of the balls?

1 Answer
Apr 17, 2016

Answer:

#color(red)(v_1^'=3/2 m/s)#
#color(red)(v_2^'=15/2)#

Explanation:

#"momentums before collision"#
#P_1=m_2*v_1=5*6=30" " kg*m/s#
#P_2=m_2*v_2=3*0=0#
#Sigma vec P_b=vecP_1+vec P_2" total momentum before collision"#

#Sigma vec P_b=30+0=30 " "kg*m/s#

#"total momentum after collision must be "30 " "kg.m/s#

#"momentums after collision"#
#vec P_1^'=m_1*v_1^'=5*v_1^'#
#vec P_2^'=m_2*v_2^'=3*v_2^'#

#Sigma P_a=vec P_1^'+vec P_2^'#
#Sigma P_a=5*v_1^'+3*v_2^'#

#Sigma vec P_b=Sigma vec P_a#

#30=5*v_1^'+3*v_2^'" "(1)"#

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

#"use the equation (1)"#

#30=5v_1^'+3(6+v_1^')#
#30=5v_1^'+18+3v_1^'#
#30-18=8v_1^'#
#12=8v_1^2#
#v_1^'=12/8#
#color(red)(v_1^'=3/2 m/s)#

#"use (2)"#
#v_2^'=6+v_1^'#
#v_2^'=6+1,5#

#color(red)(v_2^'=15/2)#