Check for me this solution in General Physic

[vuvan]

Homework Statement

I reckon that we only apply conservation of linear momentum for object which has total net force acting on equal zero but in this case , the gravity force still exist , total net force is mg
Thank in advance

Homework Equations

The Attempt at a Solution

 

[vuvan]

So i reckon the solution is wrong ? how do you think

 

[aim1732]

No the solution is right.
By impulse momentum theorem: F_avg.ext Δt + mu = mv

Since the time span of the explosion and by inference your observation is very short and gravity forces are comparatively weak,the change in net momentum of the system is very very small and hence momentum is conserved in a meaningful way.You can dispute that but thinking that physics in real life is full of approximations(you are ignoring air drag,variation of g and atmospheric pressure with altitude etc. already), it should seem reasonable.However the same is not true when the external force is impulsive or the time span of observation is big enough.