Question

A 4.8-kilogram ball moving at 8 m/sec to the right collides with a 1.4-kilogram ball at rest. After the collision, the 4.8-kilogram ball moves at 4.8 m/sec to the right. What is the velocity of the 1.4-kilogram ball?m/s

Answer 1

The final velocity of the 1.4 kg ball is 11.0 m/s to the right

Explanation:

We can solve this problem, by using the law of conservation of momentum: in fact, the total momentum of the two balls must be conserved before and after the collision. Therefore, we can write:

$p_i = p_f\\m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$

where:

$m_1 = 4.8 kg$ is the mass of the first ball

$u_1 = 8 m/s$ is the initial velocity of the first ball (taking right as positive direction)

$v_1 = 4.8 m/s$ is the final velocity of the first ball

$m_2 = 1.4 kg$ is the mass of the second ball

$u_2 = 0$ is the initial velocity of the second ball  (it is at rest)

$v_2$ is the final velocity of the second ball

And solving the equation for v2, we find:

$v_2 = \frac{m_1 u_1-m_1v_1}{m_2}=\frac{(4.8)(8)-(4.8)(4.8)}{1.4}=11.0 m/s$

So, the 1.4 kg ball moves at 11.0 m/s to the right.

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