 #1
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 8
Homework Statement:

The cannonballs have a speed of V0 = 100m/s when they exit the barrel.The sparrows sit in a nearby castle. The castle stands on a 250m high mountain (= H = level of the castle courtyard), has a 37m (= h) height of the castle wall with a thickness d = 10m.
Note: Start your calculation with x (t) and z (t).
a) At which point x0 in front of the castle does he have to set up his cannon when the inclination angle α0 of the barrel is fixed at 60∘ and he wants to touch the castle battlement in the ascending branch of the parabola?
b) Which is the heighest point of the trajectory (zmax)
c) And at which xmax do the cannoballs hit the courtyard
Relevant Equations:
 t = vo * sinα/g
Now I did what the suggestion said I started my calculation with x(t);
x(t) = v0 * cosα * t
As I was missing the t component I found it like this
t = v0 * sinα/g
t = 8,82 s
Now I've put t back into x(t) and got this result;
x(t) = 441 m
Now what I think I have gotten is the complete flight path (or length) of the cannoball in the x coordinate.
Now how do I get the x0 component out of this? The way I am looking at this is that the y component (or z in my case) doesnt have to do anything with this,meaning I can leave that out. The thickness of the wall shouldnt play a roll in this either but the part that confuses me is the height.Since the castle is on the hill can I sum up the two heights and just get one and look at it that way. Also we are given a sketch that says that the 0,0 point in the coordinate system is the castle it self, meaning that if we were to put the cannon infront of the castle,we would have to go left out the 0,0 point meaning the result would be negative? The main question is how do I calculate the x0 position of the cannon?
x(t) = v0 * cosα * t
As I was missing the t component I found it like this
t = v0 * sinα/g
t = 8,82 s
Now I've put t back into x(t) and got this result;
x(t) = 441 m
Now what I think I have gotten is the complete flight path (or length) of the cannoball in the x coordinate.
Now how do I get the x0 component out of this? The way I am looking at this is that the y component (or z in my case) doesnt have to do anything with this,meaning I can leave that out. The thickness of the wall shouldnt play a roll in this either but the part that confuses me is the height.Since the castle is on the hill can I sum up the two heights and just get one and look at it that way. Also we are given a sketch that says that the 0,0 point in the coordinate system is the castle it self, meaning that if we were to put the cannon infront of the castle,we would have to go left out the 0,0 point meaning the result would be negative? The main question is how do I calculate the x0 position of the cannon?