Answer to Question #195068 in Classical Mechanics for Jake

Question

A 360 kg roller coaster car traveling at 18 m/s collides inelastically with a stationary 240 kg car on a section of a horizontal track. To what maximum height, h, do the combined cars travel before rolling back down the hill?

Answer 1

$m_1v=(m_1+m_2)u\implies\\ u=\frac{m_1v}{m_1+m_2},$

$\frac{(m_1+m_2)u^2}{2}=(m_1+m_2)gh\implies\\ h=\frac{u^2}{2g}=\frac{m_1^2v^2}{2(m_1+m_2)^2g}=5.9~m.$