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 `30m//s` . The third pieces has three times the mass of each other piece. What is the direction (w.r.t. the piece 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` be the mass of each piece, flying off prependicular to one another with same speed `u(=30ms^(-1)` . Then `3m` is the mass of the third piece. Let `V` be the velocity of `3^(rd)` ppiece. According to figure.
`3mvcostheta=m u` , `3mvsintheta=m u` .
`tantheta=1` or `theta=45^(@)` .
`tantheta=1` or `theta=45^(@)` or `(3v)/(sqrt2)=u=30m//s` .
or `v=10sqrt(2)ms^(-1)` .
(inclineed at `135^(@)` w.r.t. direction of each one).