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 # 8 kg#. What are the post-collision velocities of the balls?

1 Answer
Jun 29, 2016

Answer:

#v_r^'=-7.27" "m/s" The red ball's velocity after collision"#
#v_b^'=8.73" "m/s" The blue ball's velocity after collision"#

Explanation:

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#"BEFORE COLLISION"#

#m_r=3" kg The red ball's mass"#
#v_r=16" "m/s " The velocity of red ball before collision"#

#P_r=m_r*v_r=16*3=48 kg*m/s#
#P_r:"(The red ball's momentum before collision)"#

#m_b=8" kg The blue ball's mass"#
#v_r=0" "m/s " The velocity of blue ball before collision"#

#P_b=m_b*v_b=8*0=0#
#P_b=0#

#P=P_r+P_b=48+0=48 kg*m/s#

#P:"(The Total momentum before collision)"#

#"AFTER COLLISION"#

#P_r^'=3*v_r^'" The red ball's momentum after collision" #
#P_b^'=8*v_b^' " The blue ball's momentum after collision"#
#P_^'=P_r^'+P_b^'#
#P^'=3*v_r^'+8*v_b^'#

#P^':"The total momentum after collision"#

#P=P^'" The conservation of momentum"#

#48=3*v_r^'+8*v_b^' " equation 1"#

#v_r+v_r^'=v_b+v_b^'" equation 2"#
#16+v_r^'=0+v_b^'#
#v_b^'=16+v_r^'" plug in equation 1"#

#48=3*v_r^'+8*(16+v_r^')#

#48=3v_r^'+128+8v_r^'#

#11v_r^'=48-128#

#11 v_r^'=-80#

#v_r^'=-80/11#

#v_r^'=-7.27" "m/s" The red ball's velocity after collision"#

#"So;"#
#v_b^'=16+v_r^'#

#v_b^'=16-7.27#

#v_b^'=8.73" "m/s" The blue ball's velocity after collision"#