A ball with a mass of #6 kg# moving at #8 m/s# hits a still ball with a mass of #12 kg#. If the first ball stops moving, how fast is the second ball moving?

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Answer 1 · 2018-04-30T18:55:22

The problem statement implies an elastic collision. Hence, the conservation of energy holds. Recall,

#1/2m_"A"nu_"A"^2+1/2m_"B"nu_"B"^2 = 1/2m_"A"nu_"A"^('2)+1/2m_"B"nu_"B"^('2)#

Given,

#m_"A" = 6"kg"#, #nu_"A" = (8"m")/"s"#, and #nu_"B"' = 0#

#m_"B" = 12"kg"#, #nu_"B" = 0#

Hence,

#1/2m_"A"nu_"A"^2 = 1/2m_"B"nu_"B"^('2)#

#=>nu_"B"' = sqrt((m_"A"nu_"A"^2)/m_"B") approx (5.6"m")/"s"#

is the speed of the second ball after the collision.