If the speed of the first fragment is 6.3 m/s,find the internal energy of the explosion.?

Question

An object initially at rest explodes in two fragments of masses 4.8 kg and 1.8 kg that move in diametrically opposite directions.

Answer 1

Energy conserved
Pe=Ke=Ke1 + Ke2=
Pe= .5(m1v1^2 + m2v2^2)

Low of conservation of momentum

m1V1' +m2v2'=m1V1+m2v2
Since initial velocities are zero
m1V1+m2v2=0

m1V1=- m2v2
and since they are moving in apposite direction we can write
m1V1=- m2v2
v2=(m1/m2)v1

then

Pe= .5(m1v1^2 + m2((m1/m2)V1)^2)