Question

5. Object A has a mass of 3 kg and is moving at 6 m/s before the collision with the 2 kg object B which is moving at -5 m/s. After the collision, object A has a velocity of 2 m/s. a. What is the total initial momentum of object A and B?b. What is the final velocity of object B after the collision?

Answer 1

Given,

The mass of object A is

$m_1=3kg$

The mass of object B is

$m_2=2kg$

The velocity of the object A before the collision is

$u_1=6\text{ m/s}$

The velocity of the object B before the collision is

$u_2=-5\text{ m/s}$

The velocity of object A after the collision is

$v_1=2\text{ m/s}$

Let the velocity of object B after the collision is v.

(a) The total initial momentum of objects A and B.

$\begin{gathered} m_1u_1+m_2u_2=(3kg)\times(6\text{ m/s)+(2 }kg)\times(-5\text{ m/s)} \\ =18-10 \\ =8 \end{gathered}$

The total initial momentum of objects A and B is 8.

(b) From the conservation of momentum,

$\begin{gathered} m_1u_1+m_2u_2=m_1v_1+m_2v_2 \\ 8=(3kg)\times(2\text{ m/s)+(2 }kg)\times v \\ 2v=8-6 \\ v=1\text{ m/s} \end{gathered}$

The final velocity of object B after the collision is 1 m/s.