A bomb explodes in air when it has a horizontal speed of `10 m//s`. It breaks into two pieces `A` and `B` of mass ratio `1 : 2`. If `A` goes vertically up at a speed of `40 m//s` , the speed of `B` is

Options

A. `20 m//s`
B. `25 m//s`
C. `30 m//s`
D. `50 m//s`

Answer

B

Explanation

By the momentum conservation
`x : 3 m xx 10 = 2 mv cos theta`
`rArr v cos theta = 15`
`y : 0 = m xx 40 + 2 mv sin theta`
`rArr v sin theta = - 20`
`v = sqrt((v sin theta)^(2) + ( v cos theta)^(2)) = 25 m//s`