Question

A bomb of mass 1 kg initially at rest, explodes and breaks into three fragments of masses in the ratio 1:1:3. The two pieces of equal masses fly off perpendicular to each other with a speed 15 m/s each. What will be the speed of heavier fragment ?

Answer 1

Masses of fragments: 1/5 * 1kg, 1/5* 1kg, 3/5 * 1kg
ie., 0.2 kg, 0.2 kg, 0.6 kg

Linear momentum of theirs:
0.2*15 m/s = 3 kg-m/s, 3 kg-m/s, 0.6 * v kg-m/s

The vector sum of the first two : 3 √2 kg-m/s as they two linear momenta are perpendicular. This will be in North East direction, if the two pieces fly off in North and East directions respectively.

So linear momentum of the large piece is in the direction of South West direction as Linear momentum of all three pieces is 0 (as before explosion).

Velocity of the third piece = 3√2 kg-m/s / 0.6 kg = 5√2 m/s


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