A shell at rest at origin explodes into three fragments of masses 1 kg, 2 kg and m kg. The fragments of masses 1 kg and 2 kg fly off with speeds `12 m//s` along x-axis and `8 m//s` along y- axis. If the m kg piece flies off with speed of `40 m//s` then find the total mass of the shell.

Explanation

As initial velocity = 0, Initial momentum
`=(1+2+m)xx0=0`
Finally, let velocity of `M=vecV`.
We know `|vecV|=40m//s`.
Initial momentum = final momentum .

`0=1xx12 hati+2xx8hatj+mvecV`
`rArr vecV= -((12hati+16hatj))/(m)`
`|vecV|=sqrt(((12)^(2)+(16)^(2))/(m^(2)))=(1)/(m)`
`sqrt((12)^(2)+(16)^(2))=40`{given}
`m=sqrt(((12)^(2)+(16)^(2))/(40))=0.5kg`
Total mass `=1+2+0.5=3.5kg`