Projectile Mass & Energy: Solving for Speed in a Cannon Carrell

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To determine the speed of a projectile with mass 2m leaving a cannon, the conservation of energy principle is applicable. The work done on both projectiles is equal since they are fired over the same distance with the same force. This implies that the kinetic energy imparted to each projectile can be analyzed using the work-energy theorem. By equating the work done to the kinetic energy of each projectile, the relationship between mass and speed can be established. Ultimately, understanding these principles will help solve for the speed of the second projectile.
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Homework Statement



If a projectile of mass m leaves the carrell of a cannon with a speed v, at what speed will a projectile of mass 2m leave the barrel.

I think i need to use conservation of energy but I am not sure how!

Thanks
 
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Hint: Since the projectiles are fired over the same length of the carrell with the same force, and since work is force times the distance in the direction of the force, then the work done on the projectiles are the same in each case. Think about the work-energy theorem. Please show your attempt.
 
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