Question

A large blue marble of mass 3.5 g is moving to the right with a velocity of 15 cm/s. The large marble hits a small red marble of mass 1.2 g that is moving to the right with a velocity of 3.5 cm/s. After the collision, the blue marble moves to the right with a velocity of 5.5 cm/s.

What is the magnitude of the final velocity of the red marble?

9.2 cm/s
14 cm/s
24 cm/s
31 cm/s

Answer 1

31

Step-by-step explanation:

edge 2021

Answer 2

31 cm/s

Step-by-step explanation:

Let's solve the problem by using conservation of momentum:

`m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2`

where:

`m_1 = 3.5 g` is the mass of the blue marble

`m_2=1.2 g` is the mass of the red marble

`u_1 = 15 cm/s` is the initial velocity of the blue marble

`u_2 = 3.5 cm/s` is the initial velocity of the red marble

`v_1 = 5.5 cm/s` is the final velocity of the blue marble

We can find the final velocity of the red marble by re-arranging the equation and solving for
`v_2`:

`v_2 = (1)/(m_2)(m_1 u_1 + m_2 u_2 - m_1 v_1)=`

`=(1)/(1.2)(3.5\cdot 15 + 1.2 \cdot 3.5 - 3.5 \cdot 5.5  )=31 cm/s`