Answer:
e).
Step-by-step explanation:
Assuming no external forces acting during the instant of the explosion, total momentum must be conserved.
As the object was initially at rest, the initial momentum is zero, which means that after the explosion, total momentum must add to zero too.
Let's call m₁ = 3 kg-piece and m₂= 6 kg-piece.
⇒ m₁*v₁ + m₂*v₂ = 0
⇒ 3kg* v₁ = -6kg*v₂
⇒ 6/3 = 2 = v₁/v₂ ⇒ v₂/v₁ = 1/2 (in magnitude)
v₂ (being the speed of the 6-kg piece) = 1/2 * v₁ (speed of thr 3-kg piece).
So, we conclude in that the statement e) is the one that is true.