Question

A body of mass 1kg initially at rest explodes and breaks into three fragments of masses in the ratio 1:1:3 . The two masses of equal masses fly off perpendicular to each other with a speed of 30m/s each.What is the velocity of the 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 * 30 m/s = 6 kg-m/s,  6 kg-m/s,  0.6 * v  kg-m/s

The vector sum of the first two :   6√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 = 6√2 kg-m/s / 0.6 kg = 10√2 m/s
           in South West dir.