A stick of dynamite (190 g) contains roughly 10 J of chemical energy that is transformed into mechanical energy and heat during an explosion.

Question

A 1000 kg rock in outer space is at rest with respect to a spaceship. An astronaut blows up the rock with one stick of dynamite. Suppose that there are only two pieces of debris after the explosion with masses m_1 = 200 kg and m_2 = 800 kg. What are the speeds of the two pieces with respect to the spaceship? (Assume that we can neglect both heat production during the explosion and the energy needed to break the rock.)