(practice exam question) An explosive shell, with total mass 80 kg is launched v

Question

(practice exam question)

An explosive shell, with total mass 80 kg is launched vertically into the air from a mortar. The shell explodes in flight and breaks into two parts with masses of 30 kg and 50 kg (assume the mass of the explosive is negligible). The portions land at the same time. The 30 kg portion of the shell lands 1000 m from the mortar. Determine where the other portion of the shell landed, explaining the physical principles that you applied to find your answer. Hint: The equation for the centre of mass of a system is:

Explanation / Answer

Since the shell is launched straight up, the only motion of the center of mass is up and down. There is no lateral motion of the center of mass. Therefore when the pieces have landed, their center of mass still has to be centered on the mortar. Center of mass is mass times distance from origin. So whatever direction the 30 kg landed -- the 50 kg landed 600 meters in the opposite direction. That is the answer to the question. If the 30 kg piece landed to the northwest, the 50 kg piece is to the southeast. Leaves center of mass unchanged. Set up your axes so the 30 kg piece has a location of (1000,0); the 50 kg piece is at (-600,0). Mass times distance gives (30)(1000) + (50)(-600) = 0 which is what it must be.

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