A ball with a mass of # 3 kg# is rolling at #16 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
May 21, 2016

Answer:

#vec v_1^'=24-16=8" "m/s#

#vec v_2^'=24" "m/s#

Explanation:

#vec P_1=m_1*vec v_1" momentum of " m_1" before collision" #

#vec P_2=m_2*v_2" momentum of " m_2 " before collision"#

#vec Sigma P_b=vec P_1+vec P_2" total momentum before collision"#

#Sigma vec P_b=m_1*vec v_1+m_2*vec v_2#

#Sigma vec P_b=3.16+1*0=48 " "kg*m/s#

#"post collision velocities :"#

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

#vec v_1^'=(2*48)/(3+1)-16#

#vec v_1^'=96/4-16#

#vec v_1^'=24-16=8" "m/s#

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

#vec v_2^'=(2*48)/(3+1)-0#

#vec v_2^'=96/4#

#vec v_2^'=24" "m/s#