A ball with a mass of # 6 kg# is rolling at #25 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
Apr 12, 2016

Answer:

#v_1^'=125/7 m/s#
#v_2^'=300/7 m/s#

Explanation:

#vec P_1+vec P_2:" total momentum before collision "#
#vec P_1^'+vec P_2^':" total momentum after collision"#
#vec P_1+vec P_2=vec P_1^'+vec P_2^'" conservation of momentum"#

#m_1*v_1+m_2*v_2=m_1*v_1^'+m_2*v_2^'#
#6*25+1*0=6*v_1^'+1*v_2^'#
#150=6*v_1^'+1*v_2^'" (1)"#

#v_1+v_1^'=v_2+v_2^'" (2)"#
#25+v_1^'=0+v_2^'#
#v_2^'=25+v_1^'" (3)"#

#"let's use (1)"#
#150=6*v_1^'+25+v_1^'#
#150-25=7v_1^'#
#125=7v_1^'#
#v_1^'=125/7 m/s#

#"let's use (3)"#
#v_2^'=25+125/7#
#v_2^'=(175+125)/7#
#v_2^'=300/7 m/s#