Answer to Question #139409 in Physics for Dave

Question

A body of mass12kg travelling at 42m/s collides with a body of mass 18kg at rest calculate their common velocity if the two bodies coalesce after coalition

Answer 1

We can find the common velocity of two bodies after the collision from the Law of Conservation of Momentum:

$$m_1v_1+m_2v_2=(m_1+m_2)v_{c},$$

here, $v_{c}$ is the common velocity of two bodies after the collision, $m_1=12\ kg$ is the mass of the first body, $v_1=42\ ms^{-1}$is the velocity of the first body, $m_2=18\ kg$ is the mass of the second body, $v_2=0\ ms^{-1}$is the velocity of the second body.

Then, from this equation we can find the common velocity of two bodies after the collision:

$$v_c=\dfrac{m_1v_1+m_2v_2}{(m_1+m_2)},$$ $$v_c=\dfrac{12\ kg\cdot 42\ ms^{-1}+18\ kg\cdot 0\ ms^{-1}}{(12\ kg+18\ kg)}=16.8\ ms^{-1}.$$

Answer:

$v_c=16.8\ ms^{-1}.$