A ball with a mass of # 5 kg# is rolling at #14 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
May 26, 2016

Answer:

#v_1^'=14/9" "m/s#

#v_2^'=140/9 " "m/s#

Explanation:

#m_1=5" " kg#
#v_1=14" " m/s#
#"Momentum before collision for the object with mass of 5 kg"#
#P_1=m_1*v_1=5*15=70" "kg*m/s#

#m_2=4" "kg#
#v_2=0#
#"Momentum before collision for the object with mass of 4 kg"#

#P_2=m_2*v_2#
#P_2=4*0=0#

#"The total momentum of objects before collision" #
#Sigma P_b=P_1+P_2#
#Sigma P_b=70+0=70#

#"Post collision velocities :"#

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

#v_1^'=(2*70)/(5+4)-14#

#v_1^'=140/9-14#

#v_1^'=(140-126)/9#

#v_1^'=14/9 " "m/s#

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

#v_2^'=(2*70)/(5+4)-0#

#v_2^'=140/9" "m/s#