A ball with a mass of #2 kg# is rolling at #6 m/s# and elastically collides with a resting ball with a mass of #1 kg#. What are the post-collision velocities of the balls?

1 Answer
Mar 1, 2016

Answer:

#v_1^'=2 m/s#
#v_2^'=8 m/s#

Explanation:

#vec P_1 + vec P_2= vec P_2^' + vec P_2^'" the conservation of momentum"#
#m_1*v_1+m_2*v_2=m_1*v_1^'+m_2*v_2^'#
#2*6+0=2*v_1^'+1*v_2^'#
#12=2*v_1^'+v_2^'" (1)"#
#v_1+v_1^'=v_2+v_2^'" (2)#
#6+v_1^'=0+v_2^'#
#v_2^'=6+v_1^'" (3)"#
#"use equation (1)"#
#12=2*v_1^'+6+v_1^'#
#12-6=3*v_1^2#
#6=3*v_1^' " " v_1^'=2 m/s#
#"use equation (3)"#
#v_2^'=6+2#
#v_2^'=8 m/s#