A ball with a mass of #2 kg # and velocity of #8 m/s# collides with a second ball with a mass of #6 kg# and velocity of #- 1 m/s#. If #20%# of the kinetic energy is lost, what are the final velocities of the balls?

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Answer 1 · 2018-03-27T16:14:40

The final velocities of the ball (assuming they stick together after collision) is #2.59# m/s.

We can start by finding the kinetic energies of each ball prior to the collision.

#KE_"mass 2kg" = 1/2mv^2 = 1/2(2)(8^2) = 64 J#

#KE_"mass 6kg" = 1/2(6)(-1)^2 = 3J#

We know from the question that

#4/5(KE_"mass 2kg" + KE_"mass 6kg") = KE_"final"#

Thus

#4/5(67) = KE_"final"#

#53.6 = KE_"final"#

#53.6 = m_"total"v^2#

#53.6 = (2 + 6)v^2#

#53.6/8 = v^2#

#v = 2.59# m/s

Hopefully this helps!