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A ball with a mass of #8 kg# moving at #14 m/s# hits a still ball with a mass of #2 kg#. If the first ball stops moving, how fast is the second ball moving?

Answer 1

56m/s.

We need to consider here the conservation of linear momentum. The law of conservation of linear momentum states that the total momentum of an isolated system is conserved, i.e., #m_1v_1 + m_2v_2 = m_1v_1^' + m_2v_2^'# where #m#'s are the masses of the two objects, #v#'s are the magnitudes of velocities before collision and #v^'#'s are the velocities of the objects after collision. We assume that the velocities are non-relativistic so that the masses remain constant.

For a perfectly inelastic collision, as is in the current problem, #v_2 = 0 & v_1^' = 0# Therefore, we have, #m_1v_1 = m_2v_2^'#.

Thus, given that #m_1 = 8kg, m_2 = 2kg# and #v_1 = 14m/s#, #v_2^' = m_1v_1/m_2 = 8**14/2 = 56m/s#.

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Answer 2

Layla Ahmed

The second ball will move at 7 m/s.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.