Question

A 1000 kg car traveling @ 30 m/s, 30 degrees S of E collides w/a 3000 kg Truck heading NE @ 20 m/s and makes the collision completely inelastic. Inelastic? Estimate the final dir then find how fast and in what dir they are traveling after the crash.

Answer 1

Sinse the collision is completely inelastic then applying the law of conservation of momentum we obtained $m_1\vec v_1+m_2\vec v_2=(m_1+m_2)\vec v$ where $m_1\vec v_1$ is the momentum of the car , $m_2\vec v_2$ is the momentum of the trac, $(m_1+m_2)\vec v$ is momentum of the composite body. Than

$v= \frac { \sqrt {(m_1^2v_1^2+m_2^2v_2^2+2m_1m_2v_1v_2\cos(\vec v_1,\vec v_2)}}{m_1+m_2}\approx17ms^{-1}$ ,$\cos(\vec v,\vec v _1)=\frac{m_1v_1+m_2v_2\cos(\vec v_1,\vec v_2)}{v(m_1+m_2)}\approx0.21$

then <$(\vec v,\vec v_1)\approx78^0$