Physics

Problem

A bomb of mass

12\,\text{kg}

at rest on level ground explodes into three pieces of masses

3\,\text{kg}

4\,\text{kg}

and

5\,\text{kg}

. Immediately after the explosion the

3\,\text{kg}

piece moves horizontally toward the east with a speed of

20\,\text{m\,s}^{-1}

, while the

4\,\text{kg}

piece moves horizontally toward the north with a speed of

15\,\text{m\,s}^{-1}

. a. (i) Determine the magnitude and direction of the velocity of the

5\,\text{kg}

piece immediately after the explosion. b. (ii) Calculate the total kinetic energy produced in the explosion. c. (iii) Find the magnitude of the momentum carried by each fragment and verify that their vector sum is zero.

Intuitive explanation

This is a conservation of momentum problem where you use the fact that the total momentum before the explosion (zero, since the bomb is at rest) must equal the total momentum after. Since the bomb breaks into three pieces moving in different directions, you need to apply momentum conservation separately for the east and north components to find the unknown velocity of the third piece. Think of it as balancing a vector equation: the momenta of the first two pieces must be exactly canceled by the third piece's momentum.

Intuitive explanation

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