A explosion of an object at rest. Momentum problem

Question

A 100 kg mass is blown apart into a 60 kg piece and a 40 kg piece (you can assume the initial velocity to be zero). After the blast, the two masses are moving apart with a relative velocity (vbf – vaf) of 60 m/s. The velocity of the 60 kg mass is

Answer 1

The center of mass remains at rest, so its speed is zero.

 

(m₁v₁ + m₂v₂)/(m₁ + m₂) = 0 ⇒

 

m₁v₁ + m₂v₂ = 0

 

m₁ = 60 kg

m₂ = 40 kg

v₂ - v₁ = 60 m/s  [Assume the smaller fragment moves faster.]

 

You can solve for both v₁ and v₂ from

 

60v₁ + 40v₂ = 0

-v₁ + v₂ = 60

 

Solve this system of 2 equations in 2 unknowns v₁ and v₂ and get

 

v₁ = -24 m/s

v₂ = 36 m/s

 

The negative sign for v₁ means it is moving in the opposite direction to v₂. 

 

|v₁| = 24 m/s is the speed of the 60 kg fragment.