A bomb moving with velocity `(40i+50j-25k)m//s` explodes into two pieces of mass ratio 1:4. After explosion the smaller piece moves away with velocity `(200i +70j +15k)m//s`. The velocity of larger piece after explosion is .

Explanation

From Law of conservation of linear momentum `Mvecu=m_(1)vec(v_(1))+m_(2)vec(v_(2)), M=5x, m_(1)=5x, m_(1)=x, m_(2)=4x`
`vecu=40hati+50hatj-25hatk ms^(-1)`,
`vec(v_(1))=(200hati+70hatj+15hatk)ms^(-1)`
here `v_(2)` is the velocity of the larger piece
`5x(40hati+50hatj-25hatk)=x(200hati+70hatj+15hatk)+4x(v_(2))`
On simplification, we get `vec(v_(2))=45hatj-35hatk`