A bomb moving with velocity `(40hati+50hatj - 25hatk)` m/s explodes into two pieces of mass ratio 1 : 4. After explosion the smaller piece moves away with velocity `(200hati + 70hatj +15hatk)m//s`.

Options

A. `45hatj-35hatk`
B. `45hati-35hatj`
C. `45hatk-35hatj`
D. `-35hati+45hatk`

Answer

(a)

Explanation

From law of conservation of energy,
Initial momentum = Final momentum
Where,
Initial momentum `=mu=mxx(40i+50j-25k)`
Final momentum = Momentum of small mass+
Momentum of larger mass
`=m_(1)v_(1)+m_(2)v_(2)`
`=(M)/(5)(200i+70j+15k)+(4)/(5)Mv`
Where,
v-Velocity of the larger piece
From equation(1),
`M(40i+50j-25k)`
`=(M)/(5)(200i+70j-15k)+(4)/(5)Mv`
`v=(5)/(4)[(40i+50j-25k)+((200i+70j+15k))/(2)]`
`=(180-140k)/(4)`
`=45j-35k`.