A ball with a mass of # 5 kg# is rolling at #3 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
Feb 4, 2016

Answer:

#v_1^'=1/3 m/s#
#v_2^'=10/3 m/s#

Explanation:

#"momentum before collision=momentum after collision"#
#m_1=3 kg; v_1=3 m/s; m_2=4 kg; v_2=0#
#P_b=m_1*v_1+m_2*v_2=5*3+4*0#
#P_b=15 "(momentum before collision)"#
#P_a=m_1*V_1^'+m_2*V_2'"(momentum after collision)"#
#P_a=5*V_1^'+4*V_2^'#
#P_b=P_a#
#15=5*V_1^'+4*V_2^' #; #equation 1#
#v_1+v_1^'=v_2+v_2^'#
#3+v_1^'=0+v_2^'#;#equation 2#
write #3+v_1^' # instead # v_2^' # in equation 1
#15=5*v_1^'+4*(3+v_1^')#
#15=5*v_1^'+12+4*v_1^'#
#15-12=9*v_1^'#
#3=9*v_1^' #
#v_1^'=1/3 m/s#
#"now use equation 2"#
#3+v_1^'=v_2^'#
#3+1/3=v_2^'#
#v_2^'=10/3 m/s#