Question

A North-going Zak has a mass of 50 kg and is traveling at 4 m/s. A South -going Zak has a mass of 40 kg and is traveling at 5 m/s. If they have a perfectly inelastic collision, what is their final velocity? What are the initial and final total kinetic energies?

Answer 1

The law of conservation of momentum for inelastic collision is as follows

m_1 v_1-m_2 v_2=(m_1+m_2 ) v_f

The final velocity

v_f=(m_1 v_1-m_2 v_2)/(m_1+m_2 )

=(50 kg×4 m/s-40kg×5 m/s)/(50kg+40kg)=0 m/s

The initial kinetic energy

KE_i=(m_1 v_1^2)/2+(m_2 v_2^2)/2

=(50 kg×(4 m/s)^2)/2+(40 kg×(5 m/s)^2)/2=900 J

The initial kinetic energy

KE_f=((m_1+m_2 ) v_f^2)/2=0