There are several assumptions made here:
1) The black lines are all tangent to the circle
2) The vertical tangent line, the red line, and the blue line are all parallel to each other
3) The green lines are perpendicular to the vertical tangent line
4) The red line bisects both green lines
5) The...
Find the formula for the height of the ball, in terms of the angle kicked (the only unknown).
Find the derivative of that formula and set equal to 0.
Solve for the angle.
Plugging that angle into the 2nd derivative should result in a negative number (a positive would indicate a minimum...
You might be interested in looking at "slip rings" as well...
http://www.moog.com/products/slip-rings/commercial-industrial-slip-rings/compact-slip-ring-capsules/sra-73540/
I just came across this post and noticed 2 errors:
1) The OP states that the tank is fixed on the rooftop 5m from the ground. This would mean that the vertical measurement from the ground to the bottom of the tank is 5m. However, the picture in Post #5 shows 5m from the ground to the top of...
So, to simplify...
Given the values D, R, H, and T, calculate the following 2 values:
A=H+T-\frac{D}{2}
and
B=\sqrt{A^2 + R^2}
Then,
\angle x=\arctan{\frac{A}{R}}+\arcsin{\frac{D}{2B}}-90
or (if you prefer),
\angle x=\tan ^{-1}{\big(\frac{A}{R}\big)}+\sin...
This isn't quite what you're referring to, but you may be interested in this anyway...
Look up Scott-T transformers to see how standard 3-phase power (where each of 3 AC waveforms lags another by 120 degrees) can be transformed into 2-phase power consisting of 2 AC waveforms that are separated...
You mis-typed the volume equation. It should read V = \pi r^2h
Well, you have 2 equations with 2 unknowns, r & h (height).
So, rearrange (solve) one equation in terms of one variable and substitute in the other equation.
That will give you 1 equation with 1 unknown, which can then be...
I found this method simpler (no quadratic):
Label the point at the center of the circle point O
Label the center of the bottom of the hole point D
Label the "corner" of the hole point E
Label the point where the circle touches the cone point F
Label the point a the (imaginary) apex of the...