A bomb of mass at rest on level ground explodes into three pieces of masses

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A bomb of mass 12 kg12\,\text{kg} at rest on level ground explodes into three pieces of masses 3 kg3\,\text{kg}, 4 kg4\,\text{kg} and 5 kg5\,\text{kg}. Immediately after the explosion the 3 kg3\,\text{kg} piece moves horizontally toward the east with a speed of 20 m s−120\,\text{m\,s}^{-1}, while the 4 kg4\,\text{kg} piece moves horizontally toward the north with a speed of 15 m s−115\,\text{m\,s}^{-1}. (i) Determine the magnitude and direction of the velocity of the 5 kg5\,\text{kg} piece immediately after the explosion. (ii) Calculate the total kinetic energy produced in the explosion. (iii) Find the magnitude of the momentum carried by each fragment and verify that their vector sum is zero.

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