A cannon fires a shell at an angle of 55.0° above the horizontal. The shell has a mass of 17.5 kg, and its initial speed as it leaves the cannon is 289 m/s. The cannon is not anchored to the ground. It is mounted on a base—a large block of wood—which is sitting on a level roadway. If the road exerts a steady kinetic friction force of 430 N on the cannon’s

sliding base, how much time does it take for the cannon to stop sliding after it fires the shell?

To find the time it takes for the cannon to stop sliding after firing the shell, we need to consider the forces acting on the cannon.

First, let's analyze the forces acting horizontally (parallel to the road). The only horizontal force is the kinetic friction force exerted by the road, which is 430 N.

Next, let's analyze the forces acting vertically (perpendicular to the road). The weight of the cannon is acting downward and can be calculated using the formula: weight = mass x acceleration due to gravity. The acceleration due to gravity is approximately 9.8 m/s^2. So, the weight of the cannon is 17.5 kg x 9.8 m/s^2 = 171.5 N.

Since the cannon is not anchored to the ground, the friction force will cause a horizontal acceleration that opposes the motion of the cannon. According to Newton's second law, the net force acting on an object is equal to its mass multiplied by its acceleration.

Now, let's find the acceleration experienced by the cannon. Using the horizontal forces, we have:

Net force = Applied force - Friction force

Since the cannon is not anchored and the applied force is zero (no external forces pushing or pulling the cannon horizontally), the net force is equal to the friction force:

430 N = ma

where 'm' is the mass of the cannon. Solving for 'a' (acceleration), we get:

a = (430 N) / (17.5 kg) ≈ 24.57 m/s^2

Now, we can use the kinematic equation: v = u + at, where:
- 'v' is the final velocity (which is zero because the cannon stops),
- 'u' is the initial velocity (which is the velocity of the cannon when the shell is fired, but this information is not given in the question),
- 'a' is the acceleration (calculated above),
- and 't' is the time.

Since 'v' is zero, the equation becomes: 0 = u + (24.57 m/s^2) * t.

Therefore, t = -u / (24.57 m/s^2)

However, we need the initial velocity 'u' of the cannon to calculate the time. Unfortunately, the question does not provide this information. Without the initial velocity, we cannot determine the time it takes for the cannon to stop sliding after firing the shell.

To solve the problem completely, we need to know the initial velocity of the cannon.