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Answer :
Final answer:
The cannon's recoil velocity is calculated using the conservation of momentum to be 4.32 m/s. The kinetic energy of the projectile at its maximum height can be calculated using the kinetic energy formula, resulting in 7.63 x 10^3 J.
Explanation:
This question involves the principles of conservation of momentum and energy.
(a) Recoil velocity of the cannon: In an isolated system with no external forces, the total momentum remains constant. Initially, the momentum is zero because nothing is moving. When the cannon fires, it propels the projectile forward and recoils back, but the total momentum still remains zero (because it is an isolated system). Using the equation M1V1 = -M2V2, where M1 and V1 is the mass and velocity of the projectile and M2 is mass of the cannon and V2 the recoil velocity, you can solve for V2 to get the recoil velocity of the cannon. In this case, you would find the recoil velocity to be about 4.32 m/s in the opposite direction of the projectile's motion.
(b) Kinetic energy of the projectile at maximum height: The projectile would be moving with a horizontal velocity at its maximum height as the vertical component of the velocity is zero here. We calculate the kinetic energy using the equation K.E. = 0.5*M*V^2, where M is mass, and V is velocity. In this case, the kinetic energy of the projectile would be 7.63 x 10^3 J.
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