Final answer:
The recoil velocity of the cannon just after firing is approximately 0.65 ft/s. The average impulsive force acting on the projectile is approximately 480,000 lb.
Step-by-step explanation:
To calculate the recoil velocity of the cannon, we can use the law of conservation of momentum. The momentum before firing is equal to the momentum after firing. The momentum before firing is given by the mass of the cannon times its initial velocity, while the momentum after firing is given by the combined mass of the cannon and projectile times the recoil velocity.
Let's calculate the recoil velocity:
Mass of the cannon (m1) = 1200 lb = 1200/32.2 slugs (1 slug = 32.2 lb).
Initial velocity of projectile (v1) = 1800 ft/s
Mass of projectile (m2) = 8 lb
Recoil velocity (v2) = ?
Using the law of conservation of momentum:
m1 * v1 = (m1 + m2) * v2
(1200/32.2) * 1800 = (1200/32.2 + 8) * v2
Solving for v2, we find that the recoil velocity of the cannon just after firing is approximately 0.65 ft/s.
To calculate the average impulsive force acting on the projectile, we can use the impulse-momentum theorem. The impulse experienced by the projectile is equal to the change in momentum of the projectile.
Impulse = change in momentum = m2 * v1
Impulsive force (F) = Impulse / time = (m2 * v1) / t
Substituting the values:
F = (8 * 1800) / 0.03
Therefore, the average impulsive force acting on the projectile is approximately 480,000 lb.