Question

A spacecraft of mass M moving with a velocity V in free space and explodes and breaks into two. After explostion a mass m of spacecraft is left stationary.what is the velocity of other part ?

Answer 1

Applying Law of conservation of momentum, Pi=MV. Pf=mv₁+(M-m)v₂. Given v₁=0 => Pf=(M-m)v₂ Fext=0 ⇒Pi=Pf ⇒MV=(M-m)v₂ ⇒v₂=$\frac{MV}{M-m}$

Answer 2

before explosion,
mass of space craft = M
velocity = V
momentum = MV

after explosion,
mass of one part = m
velocity = 0
mass of other part = M-m
velocity = v = ?
momentum = m-0 + (M-m)v =(M-m)v

conserving momentum,
MV = (M-m)v
⇒ v = MV/(M-m)

∴ Velocity of other part is MV/(M-m)