Question

Two cars make a perfectly inelastic collision at an intersection. Car 1 has a mass of 1200kg, and car 2 has a mass of 1500kg. Before the collision, car 1 was travelling at 25ms^-1 north and car 2 is travelling 15ms^-1 west.

a. Calculate the speed and direction of the wreckage immediately after the collision.

b. Calculate the amount of kinetic energy that is transformed during the collision. What forms is this energy transformed into.

Answer 1

a. $m_1v_{1x}=(m_1+m_2)u_x\to u_x=\frac{m_1v_{1x}}{m_1+m_2}=\frac{1500\cdot15}{1500+1200}=8.33\ (m/s)$

$m_2v_{2y}=(m_1+m_2)u_y\to u_y=\frac{m_2v_{2y}}{m_1+m_2}=\frac{1200\cdot 25}{1500+1200}=11.11\ (m/s)$

$u=\sqrt{8.33^2+11.11^2}=13.89\ (m/s)$

$\alpha=\tan^{-1}\frac{8.33}{11.11}=36.86°$ (west of north)

b. $\frac{(m_1+m_2)u^2}{2}+Q=\frac{m_1v_1^2}{2}+\frac{m_2v_2^2}{2}$

$\frac{(1500+1200)\cdot 13.89^2}{2}+Q=\frac{1500\cdot 15^2}{2}+\frac{1200\cdot 25^2}{2}$

$Q=283292\ (J)$

Energy is converted into heat and deformation