Question

A 14-kg object moving with a constant velocity

Answer 1

The final velocity of the 14 kg object is 1.6 m/s in the same direction

Explanation:

We can solve this problem by using the law of conservation of momentum: the total momentum of the system 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:

$m_1 = 14 kg$ is the mass of the first object

$u_1 = 5.0 m/s$ is the initial velocity of the first object

$v_1$ is the final velocity of the first object

$m_2 = 8.0 kg$ is the mass of the second object

$u_2 = 3.0 m/s$ is the initial velocity of the second object

$v_2 = 9.0 m/s$ is the final velocity of the second object

Re-arranging the equation and substituting the values, we find:

$v_1 = \frac{m_1 u_1 + m_2 u_2 - m_2 v_2}{m_1}=\frac{(14)(5.0)+(8.0)(3.0)-(8.0)(9.0)}{14}=1.6 m/s$

And the direction is the same as the initial direction, since it has the same sign.

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