A bomb in the steady state explodes into three fragments. Two fragm ents of equal masses move w ith velocity 30 m /s in m utually perpendicular direction. The mass of the third fragment is equal to five times the mass of each of these two fragm ents. Find the magnitude and direction of the velocity of this third fragment.

Options

A. `6sqrt(2) m//s, theta=45^(@)` with -x and -y direction
B. `5sqrt(2) m//s, theta=45^(@)` with +x and +y direction
C. `6sqrt(2) m//s, theta=45^(@)` with +x and -y direction
D. `5sqrt(2) m//s, theta=45^(@)` with -x and -y direction

Answer

A

Explanation

Initial momentum final momentum
`M vec( v) = mvec( v )_(1) = mvec(v ) _(2) + 5 m vec( v)_(3)`
`O= m (30hat(i) ) + m(30hat(j)) + 5 m vec_(v ) ^(3)`
`=sqrt(36+36)`
`=sqrt(72)`
`=6sqrt(2) ms^(-1)`
`tan theta = (-6)/( -6) =1`
`theta =45^(@)`
`6sqrt(2) m//s theta = 45^(@)` with - X and `-Y direction