Question

 A car with a mass of 1000 kg is moving directly East at a rate of 10 m/s collides with a 1500 kg car moving directly North at 18 m/s. If this is a perfectly inelastic collision, what is the resulting momentum and direction of the final two car mass? What is the masses velocity?

Answer 1

Given:

$v_1=10\:\rm m/s$

$v_2=18\:\rm m/s$

$m_1=1000\:\rm kg$

$m_2=1500\:\rm kg$

The law of conservation of momentum says

$$m_1v_1=p_x\\ m_2v_2=p_y$$

The magnitude of final momentum

$$p=\sqrt{p_x^2+p_y^2}=\sqrt{(m_1v_1)^2+(m_2v_2)^2}$$

$$=\sqrt{(1000\times 10)^2\!+\!(1500\times 18)^2}=28792\: \rm kg\cdot m/s$$

Direction

$$\theta=\tan^{-1}\frac{p_y}{p_x}=\tan^{-1}\frac{1500\times 18}{1000\times 10}=70^{\circ} \rm N\: of\: E$$

The velosity

$$v=\frac{p}{m_1+m_2}=\frac{28792}{1000+1500}=11.5\:\rm m/s$$