The cannonball is fired at a speed of 45 and an angle of 35 . A cannonball that was accidentally dropped from the top of the castle wall hit the moat below in 1.8 .

Incomplete.

Where is your units???

To solve this problem, we can use the principles of projectile motion. We need to find the horizontal distance traveled by the cannonball when it was fired. Here's how you can calculate it:

Step 1: Split the initial velocity into horizontal and vertical components.
The initial velocity of the cannonball can be split into its horizontal and vertical components using trigonometry. The horizontal component (Vx) is given by V0 * cos(θ), and the vertical component (Vy) is given by V0 * sin(θ), where V0 is the initial velocity (45 m/s) and θ is the angle of projection (35 degrees).

Vx = V0 * cos(θ) = 45 * cos(35)
Vy = V0 * sin(θ) = 45 * sin(35)

Step 2: Calculate the time of flight for the fired cannonball.
The time of flight (T) can be calculated using the vertical component of the velocity. The formula is T = 2 * Vy / g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).

T = 2 * Vy / g = 2 * (45 * sin(35)) / 9.8

Step 3: Find the horizontal distance traveled by the fired cannonball.
The horizontal distance (X) can be calculated using the horizontal component of the velocity and the time of flight. The formula is X = Vx * T.

X = Vx * T = (45 * cos(35)) * (2 * (45 * sin(35)) / 9.8)

Now, you can plug in the values into the formulas and calculate the horizontal distance traveled by the cannonball when fired.

Note: The information about the cannonball accidentally dropped is not needed for finding the horizontal distance traveled by the fired cannonball. If you want to calculate the time of flight and horizontal distance of the dropped cannonball, a separate calculation will be required.