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If I'm right, you want to find the value of θ that gives the highest value of y, in terms of v and x.
OK, so you want a formula like:
I know how to find the maximum range and the maximum height. I also know the trajectory equation which will tell me who to find the displacement from the origin.
Now, are you asking for the maximum
a) x (horizontal distance), which I have just shown, or
b) y (height), or
c) actual distance from origin, which would be √(x²+y²)
If an object is projected at a fixed speed of u at a variable angle theta, how would one find out the equation of the curve that shows the furthest point the trajectory can be?