Question

An object of mass 3.00 Kg, moving with an initial velocity of 5.00 i m/s, collides with and sticks to an object of mass 2.00 kg with an initial velocity -3.00 j m/s. Find the final velocity of the coposite object.

Answer 1

According to the law of conservation of impulse:

$\overrightarrow{p_1}+\overleftarrow{p_2}=\overrightarrow{p}$

or

$m_1\overrightarrow{v_1}+m_2\overleftarrow{v_2}=(m_1+m_2)\overrightarrow{v}$

In scalar form:

$m_1v_1-m_2v_2=(m_1+m_2)v$

Hence

$v=\frac {m_1v_1-m_2v_2}{m_1+m_2}$

Substitute numbers.

$v=\frac{5*3+2*3}{3+5}=\frac{21}{8}=2.625\frac{m}{s}$