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?

Options

A. `10sqrt(2), 135^(@)`
B. `10sqrt(2), 90^(@)`
C. `10sqrt(2),60^(@)`
D. `10sqrt(2), 30^(@)`

Answer

A

Explanation

Suppose `m` is the mass of each piece flying off perpendicular to one another with same speed `u=(=30m//s)`. Then `3m` is the mass of the third piece. Let `v` the velocity of the third piece.

Accoprding to Figure
`3mvcostheta="mu"3mvsintheta="mu"`
`tantheta=1`or `theta=45^(@)`
Hence `3mvcos45^(@)="mu"`
or `(3v)/sqrt2=u=30m//s` or `v=10sqrt2m//s`