A bomb of mass M at rest explodes into three pieces in the ratio 1 : 1 : 2. The

smaller ones are thrown off in perpendicular directions with velocities 3 ms−1
and 4 ms−1. What is the velocity of the third piece after the explosion?

1 answer

you need v such that

3i + 4j + 2(xi+yj) = 0
3+2x = 0
4+2y = 0

v = -3/2 i -2j
now just get the magnitude and direction.