A vessel at rest explodes breaking it into three pieces. Two pieces having equal mass fly off perpendicular to one another with the same speed of `30 m//s`. The third piece has three times the mass of each of the other two pieces. What is the direction (w.r.t. the pieces having equal masses) and magnitude of its velocity immediately after the explosion?

Explanation

For momentum conservation in each direction of motion of the smaller pieces,
`{:(3m v cos theta = m xx 30),(3m v sin theta = m xx 30):}}`
These two relations give,
`tan theta=1`, and `v=10sqrt(2)m//s`
The 3rd piece of mass 3m will go making an angle `(180-theta)=135^(@)` relative to either piece of equal masses.