Question

A missile of `M` moving with velocity `v=200m//s` explodes in midair breaking into two parts of mass `M//4` & `3M//4`. If the smaller piece flies off at an angle of `60^(@)` with respect to the original direction of motion with an initial speed of `400m//s`, what is the magnitude and direction of the initial velocity of the other piece.

Answer 1

by COLM along `x` axis:
`200M=400xx(M)/(4)cos60^(@)+(3M)/(4)Vcostheta`
`(3)/(4)vcostheta=150" "rArrvcostheta=200`...(i)
by COLM along `y` axis:
`0=400(M)/(4)sin60^(@)-(3M)/(4)Vsintheta`
`3vsintheta=(400sqrt3)/(2)`
`vsintheta=(200)/(sqrt3)`...(ii)
(ii)/(i) given
`tantheta=(1)/(sqrt3)`
`rArr" "theta=30^(@)`
`rArr" "v=(400)/(sqrt3)m//s`