a cannon fires at a castle. the walls are 9m high. if the cannon is pointed at an angle of 60 degrees and has a muzzle velocity of 35m/s will the cannon balls go over the wall or hit the wall?

You need to specify how far the cannon is from the wall. The answer will depend upon it.

There is a vertical velocity component of
Vyo = 35 sin 60 = 25.98 m/s.
The cannonball can rise to a height

H = (V sin 60)^2/(2g) = 34.4 m

Surely the cannonball will clear the wall if the cannon is neither too close nor too far away.

To determine whether the cannonball will go over the wall or hit the wall, we need to analyze the projectile motion of the cannonball.

Let's break down the problem step by step:

1. Firstly, calculate the vertical component of the cannonball's initial velocity. We can use trigonometry to find this value:
Vertical component = initial velocity * sin(angle)
Vertical component = 35 m/s * sin(60°)
Vertical component ≈ 30.27 m/s

2. Next, calculate the time it takes for the cannonball to reach the topmost point of its trajectory. We can use the vertical component of velocity and the acceleration due to gravity for this calculation:
Time = vertical component / (acceleration due to gravity)
Time = 30.27 m/s / (9.8 m/s^2)
Time ≈ 3.09 seconds

3. Now, find the maximum height reached by the cannonball using the following formula:
Maximum height = (vertical component)^2 / (2 * acceleration due to gravity)
Maximum height = (30.27 m/s)^2 / (2 * 9.8 m/s^2)
Maximum height ≈ 92.79 meters

Since the maximum height of the cannonball's trajectory is 92.79 meters, which is greater than the height of the castle wall (9 meters), we can conclude that the cannonball will go over the wall and will not hit it.