Question

A 10.00 kg mass is moving to the right with a velocity of 14.0 m/s. A 12.0 kg mass is moving to the left with a velocity of 8.00 m/s. Assuming that these two balls have a head on collision and stick together, what will be the final velocity of the combination?

Answer 1

2 m/s

Step-by-step explanation:

From the conservation of momentum, the initial momentum of the system must be equal to the final momentum of the system.

Let the 10.00 kg mass be
`m_1` and the 12.0 kg mass be
`m_2`. When they collide and stick, they have a combined mass of
`m_1+m_2`.

Momentum is given by
`p=mv`. Set up the following equation:

`\displaystyle m_1v_1+m_2v_2=(m_1+m_2)v_f`, where
`v_f` is the desired final velocity of the masses.

Call the right direction positive. To indicate the 12.0 kg object is travelling left, its velocity should be substitute as -8.00 m/s.

Solving yields:

`10\cdot 14 + 12\cdot (-8)=(10+12)v_f\\\implies v_f=\boxed{2 \text{ m/s}}`