Solve physics problem using trigonometry knowing what are you doing

[blob84]

Homework Statement

http://img94.imageshack.us/img94/3053/ph1d.png


How does he get y_i=R-Rcos(theta)?

The Attempt at a Solution

if we get two triangles HBC and AHC, Rcos(theta)=AH, AB=AH+BH and AB-BH=AH=y_i.

 

[voko]

What are A, B, C and H? Also, what is the total height from the floor to the top of the rope?

 

[azizlwl]

What is the lowest level the actor can go?
This level is zero PE reference.

 

[blob84]

AHC and HBC are two triangles that we get if we draw a line from the bottom of R to the floor and by the cosine theorem we get y_i=AB-BH,
there isn't the total height.

 

[azizlwl]

Lowest level is R from top when θ=0°.
At y_i, from top is Rcosθ
mgh=1/2mv²
h=R-Rcosθ

v_2f=2g(R-Rcosθ)

 

[voko]

If $y_i$ is really defined as the distance from the floor to the end of rope of length $R$ hanging from an UNKNOWN height, then the text is incorrect, $y_i$ cannot be given any value FROM THE GEOMETRY of the problem, it is just undefined.

If it is defined FROM THE PHYSICS of the problem, then it should be defined as height from the lowest possible point, then it is what is given in the text. But the picture is INCORRECT in this case, unless the lowest point is the floor - which makes the subsequent determination of the force incorrect.