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Answer :
Final Answer:
The recoil speed of the cannon after firing the cannonball is approximately 1.30 m/s in the opposite direction of the fired cannonball.
Explanation:
To determine the recoil speed and direction of the cannon, we can use the principle of conservation of momentum. The total momentum before firing must equal the total momentum after firing.
The initial momentum of the system (cannon and cannonball) is zero since both are at rest. The final momentum of the system is the sum of the momentum of the cannonball and the cannon after firing.
Let:
- The mass of the cannon (M) be 115 kg.
- The mass of the cannonball (m) be 10.0 kg.
- The initial velocity of the cannonball (u) be 0 m/s.
- The final velocity of the cannonball after firing (v) be 90.0 m/s.
- The final velocity of the cannon (V) be the recoil speed we want to find.
- The direction of motion is chosen such that the cannonball's motion is positive, and the cannon's motion is negative (opposite direction).
Using the conservation of momentum:
0 = (m * v) + (M * V)
Substituting the values:
0 = (10.0 kg * 90.0 m/s) + (115 kg * V)
Now, solve for V:
V = - (10.0 kg * 90.0 m/s) / 115 kg
V ≈ -1.30 m/s
The negative sign indicates that the cannon moves in the opposite direction of the fired cannonball. Therefore, the recoil speed of the cannon after firing is approximately 1.30 m/s, and its direction is opposite to the fired cannonball's direction.
Understanding this concept of momentum conservation is essential in physics and engineering to analyze the motion of objects in systems.
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