What is the kinetic energy of the piece of mass

[a150daysflood]

Homework Statement

A body, initially at rest, explodes into two pieces of mass 2M and 3M respectively, having a total kinetic energy E.
What is the kinetic energy of the piece of mass 2M after the explosion?

Homework Equations

0.5mv²=K.E

The Attempt at a Solution

The velocity of the 2 pieces of objects is different,how do i calculate?
Can anyone guide me on how to start?
0.5(2m)(v_1)² + 0.5(3m)(v_2)²=E
How do i proceed?
Thanks for reading,thinking,replying.

 

[Doc Al]

Hint: During an explosion, what physical quantity (if any) of all the pieces is conserved?

 

[a150daysflood]

Solution

using conservation of momentum,
0=2mu + 3m(-v)
2mu=3mv
2u=3v
u=3v/2

Total K.E
=1/2(2m)(3v/2)² + 1/2(3m)(v)²
=15/4(m)(v²)
=E

K.E for mass of 2m:
1/2(2m)(3v/2)²
=9v²m/4

Hence,K.E for 2m is 3m/5.
Okies thanks.

 

[Doc Al]

Hence,K.E for 2m is 3m/5.

You mean KE = (3/5)E.