Projectile motion: determine launch angle

[justsway17]

Homework Statement

A cannon is supported one meter above the top of a 20 degree declining slope of length 200m. The cannon has a launch velocity of 55m/s. There is a ball halfway down this slope moving at a constant velocity of 20m/s.

-Determine the angle \Theta required for the projectile to hit the bottom of the hill within one degree.
-How long does the projectile take to hit the bottom of the hill?
-There is a target moving at a constant velocity of 20m/s down the hill. How long should you delay firing to hit the target as it reaches the bottom of the hill?
-Find the maximum distance this projectile can travel as measured from the bottom of the hill.

Homework Equations

x=x_{0}+v_{0x}t
v_{y}=v_{0y}t-gt^{2}
y=y_{0}+v_{0y}t-0.5gt^{2}
v^{2}_{y}=v^{2}_{0y}-2g(y-y_{0})

The Attempt at a Solution

I have tried using all of the two-dimensional kinematics equations with some success but the problem is that \Theta is unknown so I can't find t or v_{fy}.

My best attempts are as so:
v_{yf}=55sin\Theta-9.81t
188=55cos(\Theta)t
188=0+55cos(\Theta)t-4.9t^{2}

The diagram for the problem is attached.
Either it is algebra more complicated than I am used to or I am missing something very simple. I am confident that if I could solve for \Theta OR t I could finish the problem easily. I can't seem to get a solveable equation. Thank you for your help and I apologize if there are syntax errors as I am a first time user.

 

[yands]

There is inconsistency , the questions on the attachment and the problem statement you provided . I would like to help you but there are some ambiguity .

 

[justsway17]

I apologize for that. I just updated the post to match the wording of the diagram exactly. I have continued to work on this problem and used a few pages of paper, but still have not been able to find a way to solve for theta.

 

[yands]

You have to find the range in terms of the initial angle then try to optimize it . That is how I solved it . You have to think why one needs an optimization approach to solve this problem.