Question

A 1.3-ton sedan car travellng west at 72 km/h runs into a 2.5-ton SUV travelling south at 36 km/h at an intersection. Given that the cars stick together after the collision, their speed and the direction are:

Answer 1

The law of conservation of momentum gives

$$m_1v_1=(m_1+m_2)v \cos\theta$$

$$m_2v_2=(m_1+m_2)v \sin\theta$$

So

$$\tan\theta=\frac{m_2v_2}{m_1v_1}=\frac{2500\:\rm{kg}\times 10\:\rm{m/s}}{1300\:\rm{kg}\times 20\:\rm{m/s}}=0.9615$$

$$\theta=43.9^{\circ}\quad\rm{(south\: of\: west)}$$

$$v=\frac{1}{m_1+m_2}\sqrt{(m_1v_1)^2+(m_2v_2)^2}$$

$$=\frac{1}{1300\:\rm{kg}+2500\:\rm{kg}}\sqrt{(1300\:\rm{kg}\times 20\:\rm{m/s})^2+(2500\:\rm{kg}\times 10\:\rm{m/s})^2}$$

$$=9.5\:\rm{m/s}=34\:\rm{km/h}$$