A Medieval Knight attacking w/ a Cannon

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Anyone mind helping me strategically picking apart this word problem? I am taking physics for the first time in college and its kicking my ***, any insight on how to pick apart a problem like this and find an appropriate answer? Thank you for your time!


Assume you are a Medieval knight attacking a castle with a cannon. The ball leaves the cannon with a speed of 43.3 m/s. The barrel's angle with respect to the ground is 45.7°, and you make a perfect hit on the tyrant's chamber which is at the same level as the cannon's muzzle. What is the time of flight of the cannon ball?
 
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The 'trick' is that you can consider the horizontal and vertical motion separately.
So just consider the ball being thrown up and coming down - what acceleration do you expect, what equations do you know for a moving object.
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.

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