A cannon of mass 5.70 103 kg is rigidly bolted to the earth so it can recoil onl

Question

A cannon of mass 5.70 103 kg is rigidly bolted to the earth so it can recoil only by a negligible amount. The cannon fires an 84.5-kg shell horizontally with an initial velocity of +585 m/s. Suppose the cannon is then unbolted from the earth, and no external force hinders its recoil. What would be the velocity of an identical shell fired by this loose cannon? (Hint: In both cases assume that the burning gunpowder imparts the same kinetic energy to the system. Enter your answer to the nearest whole number. Indicate the direction with the sign of your answer.)

I have tried the answer 583.4 m/s and it said it was incorrect, I cant figure this quesiton out.

Explanation / Answer

when cannon is bolted,

Energy of system = 5700 x 0   +    84.5 x 585^2 /2    = 14459006.25 J

This is energy given by gunpowder that will be constant.

for the case when casnnon is not bolted.

using momentum conservation,

0 = 5700V - 84.5v

V = recoil speed of cannon.

V = 0.0148v

using energy conservation,

energy of this system = 5700V^2 /2   + 84.5v^2/2

= 5700 ( 0.0148v)^2 /2 + 84.5v^2 /2

= 42.876v^2

this energy will be given by gun powder.

42.876v^2   = 14459006.25

v = 580.71 m/s

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