Question

Mira and her twin sister Joy have a combined mass of 250.0 kg and are zooming along in a 150.0 kg amusement park bumper car at 15.0 m/s. They bump Miguel`s car, which is sitting still. Miguel has a mass of 45.0 kg. After the elastic collision, the twins continue ahead with a speed of 6.12 m/s. How fast is Miguel`s car bumped across the floor?

Answer 1

Apply momentum conservation:

$$(m_t+M)v=(m_t+M)u_1+(m_M+M)u_2,\\\space\\ u_2=\frac{(m_t+M)(v-u_1)}{m_M+M}=\frac{(250+150)(15-6.12)}{45+150}=18.2\text{ m/s}.$$