The captain sinks a ship located x distance away with a cannon located on the top of a cliff that is 65m high. if the cannon ball has a velocity of 55m/s and the captain sinks the ship, how far was the ship from the base of the cliff.

I got 731.5 meters. is that right?

ASSUMING the cannon direction was horizontal, and neglect air resistance.

Time to free-fall 65m, t:
65 = ut+(1/2)gt²
u=0 (initial vertical velocity)
t=√(65*2/9.81)=3.64 s.

Horizontal distance = 3.64*ux
= 3.64*55
= 200.2m

Can you explain how you got 731.5m?

I do not know in what direction the cannon was aimed, particularly, the elevation.

Assuming horizontal, and no one would shoot a cannon horizontal, but

time to fall 65m...
65=1/2 g t^2 or
t= sqrt 130/9.8= 3.64sec

distance horizontal= 55m/s*3.64 which is not your answer.

To find the distance of the ship from the base of the cliff, we can use projectile motion equations.

First, let's analyze the initial vertical motion of the cannonball. Since the cannonball is shot horizontally, there is no initial vertical velocity. The only force acting on it in the vertical direction is gravity, causing it to fall downwards.

We can use the equation for the vertical position of an object undergoing constant acceleration:

h = ut + (1/2)gt^2

Where:
h = vertical displacement
u = initial vertical velocity (0 in this case)
g = acceleration due to gravity (-9.8 m/s^2)
t = time

The cliff height will be the vertical displacement, h, equal to 65m:

65 = 0 * t + (1/2) * (-9.8) * t^2
65 = (-4.9) * t^2

Solving for t will give us the time it takes for the cannonball to fall from the top of the cliff to the base. Taking the positive root of the equation since time cannot be negative:

t = √(65 / 4.9) ≈ 3.208 seconds

Now, to find the horizontal distance, we can use the equation:

d = v * t

Where:
d = horizontal distance
v = horizontal velocity (55 m/s)
t = time (3.208 s)

Plugging in the values:

d = 55 * 3.208
d ≈ 176.44 meters

Therefore, the ship was approximately 176.44 meters away from the base of the cliff when it was sunk. So, your calculation of 731.5 meters is not correct.