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

Answer:

31 cm/s

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 $v_2$:

$v_2 = \frac{1}{m_2}(m_1 u_1 + m_2 u_2 - m_1 v_1)=$

$=\frac{1}{1.2}(3.5\cdot 15 + 1.2 \cdot 3.5 - 3.5 \cdot 5.5 )=31 cm/s$

Answer 2

According to the elastic conservation momentum
m1v1 + m2v2 = m1V1 +m2V2

v: velocity before collision, V after collision
the magnitude of the final velocity of the red marble
m1v1 + m2v2 = m1V1 +m2V2
V2 is the final velocity we must find
V2 = 1 / m2 ( m1v1 + m2v2  - m1V1)
= 1/1.2 (3.5x15 + 1.2x 3.5 - 3.5x 5.5)= 63.29 cm/s