Quote:
Originally Posted by Symph
I have revised the entire proof, sorry about the inconvenience, it should be sound now. However, considering the fact that I was thinking precisely that same thing last time I submitted this, I would encourage you to feel free to check my math again!
What say you, Ether?
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This time around I didn't review all your steps again. Instead I did the following two things:
Thing1:
I took your "final answer" of V=29.53 f/s, angle=39 degrees, launch height = 3.61042 feet and calculated the trajectory from that. Your apex occurs at x=13.2555 ft and Rs is 11.3 ft.
Here's the equation for the trajectory using 29.53 f/s & 39 degrees:
y = -0.0305452*x^2 + 0.809784*x + 3.6104
(x is horizontal distance from launch point and y is height above floor)
Thing2:
I did my own calculation to find launch speed and angle to get the desired Rs=13.5 feet.
The result is
launch speed = 31.970 ft/sec at launch angle 35.55 degrees
The trajectory using those numbers is
y = -0.0237769*x^2 + 0.714568*x + 3.6104
max height above floor = 8.9792ft @ 15.0265ft from launch point
Bottom line: whatever you're doing is certainly close enough engineering-wise for FRC application. Mathematically, I suspect you are getting some round-off error due to the calculation method you used.
PS: You forgot to edit your original post. It still says "42.5 feet per second" and "13.5" ft scoring range.