Conservation of Momentum in an Explosive Collision

[avenkat0]

Homework Statement

A 6.91x106 kg spherical spaceship in deep space explodes into two pieces, one 4.77 times the mass of the other.
a) Suppose the ship is initially at rest, and after the explosion the smaller piece is moving 57.6 m/s.
- Find the speed of the larger piece.
-Find the energy supplied by the explosion.

Homework Equations

M₁V₁+M₂V₂=0

The Attempt at a Solution

I tried establishing a ratio of the masses equals the ratio of the velocities and got -12.075 m/s for the larger piece. but got it wrong,
and the second question needs .5(m)(v²) but i don't know the velocity of the heavier mass.
Is there a flaw in my reasoning

Thanks for your help

 

[Doc Al]

I tried establishing a ratio of the masses equals the ratio of the velocities and got -12.075 m/s for the larger piece. but got it wrong,

Looks OK to me, except for the minus sign. (Speed is just a magnitude, thus always positive.)

 

[avenkat0]

I tried the answer it says its wrong... and then...
c) Suppose the ship is initially moving at constant velocity +18.2 m/s. After the explosion, the smaller piece is moving -57.6 m/s (in the opposite direction to the initial velocity), Find the velocity of the larger piece.

i tried it the same way but with starting momentum 18.2(Mtotal)... and got +9.94... and it says this is wrong as well
is my reasoning flawed? and i double checked my calculations... HELP