Is 2D Conservation of Momentum Possible? A Visual Analysis

[Saptarshi Sarkar]

Homework Statement

A high-velocity missile, travelling in a horizontal line with a kinetic energy of 3.0 Giga-Joules (GJ), explodes in flight and breaks into two pieces A and B of equal mass. One of these pieces (A) flies off in
a straight line perpendicular to the original direction in which the missile was moving and its kinetic energy is found to be 2.0 GJ. If gravity can be neglected for such high-velocity projectiles, it follows
that the other piece (B) flew off in a direction at an angle with the original direction of

Relevant Equations

$p = \sqrt {2mK.E.}$

I am unable to find any angle for which the horizontal and vertical components of the linear momentum are conserved.

I have added an image of my attempt

 

[BvU]

Conclusion ? The exercise composer is attempting to trick you ?

 

[Saptarshi Sarkar]

Conclusion ? The exercise composer is attempting to trick you ?

Maybe! The question itself seems weird. The COM of the system can no way stay in the same path, but it must.

 

[Orodruin]

What makes you think kinetic energy is conserved?

 

[gneill]

Where did the $10^9$ come from:

Edit: Oops, I see that @Orodruin beat me to the punch!

 

[Saptarshi Sarkar]

Thanks a lot for the help! I had a second attempt at the question and this the answer I arrived at.

 

[Orodruin]

Looks fine apart from all the missing units.

 

[PeroK]

Instead of numbers and units you could simply use $E_0$ and $\frac 2 3 E_0$ for the given energy.