Question

An object initially at rest breaks into two pieces as the result of an explosion. One piece has twice the energy of the other piece. What is the ratio of the masses of the two pieces? Which piece has the larger mass?

Answer 1

m₁V₁ = m₂V₂ 
KE = ½mV² 
½m₁V₁² = 2*½m₂V₂² 

m₁V₁ = m₂V₂ 
½m₁V₁² = m₂V₂² 

m₁/m₂ = V₂/V₁ 

m₁/m₂ = 2V₂²/V₁² 
V₂/V₁ = √(½m₁/m₂) 


m₁/m₂ = √(½m₁/m₂) 
squaring
(m₁/m₂)² = ½m₁/m₂ 

2m₂m₁² = m₁m₂² 
divide by m₁m₂ 
2m₁ = m₂ 
m₂/m₁ = 2 
hope this helps