A 1175-kg cannon shoots a 33-kg shell at an angle of 25° above the horizontal and a speed of 495 m/s. What is the recoil velocity of the cannon? (Take the direction the cannon is firing to be the positive direction. Indicate the direction with the sign of your answer.)
To find the recoil velocity of the cannon, we can use the principle of conservation of momentum. According to this principle, the total momentum before the cannon is fired is equal to the total momentum after the cannon is fired.
The momentum of an object is defined as the product of its mass and velocity. In this case, the momentum before firing can be calculated as the sum of the momentum of the cannon and the momentum of the shell.
The momentum of the cannon is equal to the product of its mass and velocity, which can be given as:
Momentum of cannon = mass of cannon x velocity of cannon
Similarly, the momentum of the shell can be calculated as:
Momentum of shell = mass of shell x velocity of shell
Since the shell is initially at rest before being fired, its initial velocity is 0. Therefore, the momentum of the shell is 0.
According to the conservation of momentum principle, the total momentum before the cannon is fired should be equal to the total momentum after the cannon is fired. Therefore, we can write the equation:
Momentum before = Momentum after
(mass of cannon x velocity of cannon) = (mass of shell x velocity of shell) + (mass of cannon x recoil velocity)
Plugging in the given values:
(1175 kg x velocity of cannon) = (33 kg x 0 m/s) + (1175 kg x recoil velocity)
Since the shell has no initial velocity, we can simplify the equation to:
1175 kg x velocity of cannon = 1175 kg x recoil velocity
Now, we can solve for the recoil velocity:
recoil velocity = (1175 kg x velocity of cannon) / 1175 kg
Since the velocity of the cannon is positive (the direction of firing is considered positive), the recoil velocity will also be a positive value.
Therefore, the recoil velocity of the cannon is equal to the velocity of the cannon.