A 530 cannon fires a 12 cannonball with a speed of 200 relative to the muzzle. The cannon is on wheels that roll without friction.
Incomplete.
To solve this question, we can use the principle of conservation of momentum. The total momentum before the cannonball is fired is equal to the total momentum after it is fired.
First, let's calculate the initial momentum of the system. The total mass of the system (cannon + cannonball) is the sum of the mass of the cannon (m1) and the mass of the cannonball (m2).
m1 = 530 kg (mass of the cannon)
m2 = 12 kg (mass of the cannonball)
The initial velocity of the cannonball relative to the muzzle is given as 200 m/s. Since the cannon is on wheels that roll without friction, we can assume that the cannon doesn't move horizontally when firing the cannonball. Therefore, the initial velocity of the cannon (v1) is 0 m/s.
Now, let's calculate the final momentum of the system. After the cannonball is fired, the cannon will recoil with some velocity (v2) in the opposite direction of the cannonball's velocity.
Since we know the mass and initial velocity of the cannonball, we can calculate its momentum (p2):
p2 = m2 * v2
The cannon will also have momentum in the opposite direction, given by:
p1 = m1 * v1
Since the total momentum is conserved, we can equate the sum of the initial momentum (p1) and the final momentum (p2) to zero:
p1 + p2 = 0
Substituting the values, we have:
m1 * v1 + m2 * v2 = 0
Since v1 is 0 m/s, the equation simplifies to:
m2 * v2 = 0
Now, we can solve for v2, which is the velocity at which the cannon recoils:
v2 = 0 / m2 (since m2 cannot be 0)
= 0 m/s
Therefore, the velocity at which the cannon recoils is 0 m/s. This means that there is no recoil velocity, and the cannon remains stationary when the cannonball is fired.
To summarize:
- The cannonball has a speed of 200 m/s relative to the muzzle.
- The cannon, which is on wheels that roll without friction, remains stationary when the cannonball is fired.