A spaceship travelling along `+y` axis with speed `v_(0)` suddenly shoots out one fourth of its parts with speed `2v_(0)` along `+x`-axis. `xy` axes are fixed with respect to ground. The velocity of the remaining part is

Answer

`(sqrt(13))/(2)v_(0)`

Explanation

Using conservation of momentum
Along `x` axis`rarr0=-(2M)/(3)v_(x)+(M)/(3)2v_(0)rArrv_(x)=v_(0)`
Along `y` axis `rarr Mv_(0)=(2M)/(3)v_(y)rArrv_(y)=(3)/(2)v_(0)`
`rArrv=sqrt(v_(x)^(2)+v_(y)^(2))=(sqrt(13))/(2)v_(0)`